{"id":3615,"date":"2025-09-02T19:06:06","date_gmt":"2025-09-02T19:06:06","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3615"},"modified":"2026-01-12T19:37:32","modified_gmt":"2026-01-12T19:37:32","slug":"polynomial-functions-background-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/polynomial-functions-background-youll-need-3\/","title":{"raw":"Polynomial Functions: Background You'll Need 3","rendered":"Polynomial Functions: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Create and evaluate a sign chart<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 class=\"text-2xl font-bold mt-1 text-text-100\">Create and Evaluate a Sign Chart<\/h2>\r\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<h3>sign chart<\/h3>\r\nA sign chart is a visual tool that helps us determine where polynomial expressions are positive, negative, or zero by testing values in different intervals created by the polynomial's zeros.\r\n\r\n<\/section>\r\n<p class=\"whitespace-normal break-words\">A sign chart displays the sign (positive or negative) of a polynomial expression across different intervals on the number line. A polynomial can only change signs when it equals zero.<\/p>\r\n\r\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\">\r\n<p class=\"whitespace-normal break-words\"><strong>How to: create a sign chart<\/strong><\/p>\r\n\r\n<ol>\r\n \t<li class=\"whitespace-normal break-words\"><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">Factor the polynomial completely<\/span><\/li>\r\n \t<li class=\"whitespace-normal break-words\">Find all zeros (where factors equal zero)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Mark these zeros on a number line to create intervals<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Test a value from each interval<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Record the sign of each factor and the overall polynomial<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p class=\"whitespace-normal break-words\">Create a sign chart for [latex]f(x) = (x + 2)(x - 1)(x - 4)[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">[latex] \\begin{align} \\text{Step 1: } &amp;\\text{Expression is already factored: } (x + 2)(x - 1)(x - 4) \\\\ \\text{Step 2: } &amp;\\text{Find zeros by setting each factor equal to zero:}\\\\ &amp;x + 2 = 0 \\Rightarrow x = -2\\\\ &amp;x - 1 = 0 \\Rightarrow x = 1\\\\&amp;x - 4 = 0 \\Rightarrow x = 4\\\\ \\text{Step 3: } &amp;\\text{Zeros are: } x = -2, 1, 4 \\end{align} [\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">Step 4: Create intervals and test values<\/p>\r\n<p class=\"whitespace-normal break-words\">The zeros divide the number line into four intervals:<\/p>\r\n<p class=\"whitespace-normal break-words\">[latex]\\\\ \\begin{align} (-\\infty, -2): &amp;\\quad \\text{Test } x = -3\\\\ (-2, 1): &amp;\\quad \\text{Test } x = 0\\\\ (1, 4): &amp;\\quad \\text{Test } x = 2\\\\ (4, \\infty): &amp;\\quad \\text{Test } x = 5 \\end{align} [\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">Step 5: Evaluate each factor at test points<\/p>\r\n\r\n<table class=\"bg-bg-100 min-w-full border-separate border-spacing-0 text-sm leading-[1.88888] whitespace-normal\" style=\"width: 100.063%;\">\r\n<thead class=\"border-b-border-100\/50 border-b-[0.5px] text-left\">\r\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\r\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">Interval<\/th>\r\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">Test Value<\/th>\r\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](x+2)[\/latex]<\/th>\r\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](x-1)[\/latex]<\/th>\r\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](x-4)[\/latex]<\/th>\r\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">[latex]f(x)[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](-\\infty, -2)[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = -3[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](-3+2)[\/latex] \u2192 \u2212<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](-3-1)[\/latex] \u2192 \u2212<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](-3-4)[\/latex] \u2192 \u2212<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(\u2212)(\u2212)(\u2212) = \u2212<\/td>\r\n<\/tr>\r\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](-2, 1)[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = 0[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](0+2)[\/latex] \u2192 +<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](0-1)[\/latex] \u00a0\u2192 \u2212<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](0-4)[\/latex] \u2192 \u2212<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(+)(\u2212)(\u2212) = +<\/td>\r\n<\/tr>\r\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](1, 4)[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = 2[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](2+2)[\/latex] \u2192 +<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](2-1)[\/latex] \u00a0\u2192 +<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](2-4)[\/latex] \u2192 \u2212<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(+)(+)(\u2212) = \u2212<\/td>\r\n<\/tr>\r\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](4, \\infty)[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = 5[\/latex]<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](5+2)[\/latex] \u2192 +<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](5-1)[\/latex] \u2192 +<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](5-4)[\/latex] \u2192 +<\/td>\r\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(+)(+)(+) = +<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]311019[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Create and evaluate a sign chart<\/span><\/li>\n<\/ul>\n<\/section>\n<h2 class=\"text-2xl font-bold mt-1 text-text-100\">Create and Evaluate a Sign Chart<\/h2>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<h3>sign chart<\/h3>\n<p>A sign chart is a visual tool that helps us determine where polynomial expressions are positive, negative, or zero by testing values in different intervals created by the polynomial&#8217;s zeros.<\/p>\n<\/section>\n<p class=\"whitespace-normal break-words\">A sign chart displays the sign (positive or negative) of a polynomial expression across different intervals on the number line. A polynomial can only change signs when it equals zero.<\/p>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\">\n<p class=\"whitespace-normal break-words\"><strong>How to: create a sign chart<\/strong><\/p>\n<ol>\n<li class=\"whitespace-normal break-words\"><span style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">Factor the polynomial completely<\/span><\/li>\n<li class=\"whitespace-normal break-words\">Find all zeros (where factors equal zero)<\/li>\n<li class=\"whitespace-normal break-words\">Mark these zeros on a number line to create intervals<\/li>\n<li class=\"whitespace-normal break-words\">Test a value from each interval<\/li>\n<li class=\"whitespace-normal break-words\">Record the sign of each factor and the overall polynomial<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p class=\"whitespace-normal break-words\">Create a sign chart for [latex]f(x) = (x + 2)(x - 1)(x - 4)[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">[latex]\\begin{align} \\text{Step 1: } &\\text{Expression is already factored: } (x + 2)(x - 1)(x - 4) \\\\ \\text{Step 2: } &\\text{Find zeros by setting each factor equal to zero:}\\\\ &x + 2 = 0 \\Rightarrow x = -2\\\\ &x - 1 = 0 \\Rightarrow x = 1\\\\&x - 4 = 0 \\Rightarrow x = 4\\\\ \\text{Step 3: } &\\text{Zeros are: } x = -2, 1, 4 \\end{align}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">Step 4: Create intervals and test values<\/p>\n<p class=\"whitespace-normal break-words\">The zeros divide the number line into four intervals:<\/p>\n<p class=\"whitespace-normal break-words\">[latex]\\\\ \\begin{align} (-\\infty, -2): &\\quad \\text{Test } x = -3\\\\ (-2, 1): &\\quad \\text{Test } x = 0\\\\ (1, 4): &\\quad \\text{Test } x = 2\\\\ (4, \\infty): &\\quad \\text{Test } x = 5 \\end{align}[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">Step 5: Evaluate each factor at test points<\/p>\n<table class=\"bg-bg-100 min-w-full border-separate border-spacing-0 text-sm leading-[1.88888] whitespace-normal\" style=\"width: 100.063%;\">\n<thead class=\"border-b-border-100\/50 border-b-[0.5px] text-left\">\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">Interval<\/th>\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">Test Value<\/th>\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](x+2)[\/latex]<\/th>\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](x-1)[\/latex]<\/th>\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](x-4)[\/latex]<\/th>\n<th class=\"text-text-000 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">[latex]f(x)[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](-\\infty, -2)[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = -3[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](-3+2)[\/latex] \u2192 \u2212<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](-3-1)[\/latex] \u2192 \u2212<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](-3-4)[\/latex] \u2192 \u2212<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(\u2212)(\u2212)(\u2212) = \u2212<\/td>\n<\/tr>\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](-2, 1)[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = 0[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](0+2)[\/latex] \u2192 +<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](0-1)[\/latex] \u00a0\u2192 \u2212<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](0-4)[\/latex] \u2192 \u2212<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(+)(\u2212)(\u2212) = +<\/td>\n<\/tr>\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](1, 4)[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = 2[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](2+2)[\/latex] \u2192 +<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](2-1)[\/latex] \u00a0\u2192 +<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](2-4)[\/latex] \u2192 \u2212<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(+)(+)(\u2212) = \u2212<\/td>\n<\/tr>\n<tr class=\"[tbody&gt;&amp;]:odd:bg-bg-500\/10\">\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 13.7464%;\">[latex](4, \\infty)[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 10.2577%;\">[latex]x = 5[\/latex]<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.1805%;\">[latex](5+2)[\/latex] \u2192 +<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 17.2934%;\">[latex](5-1)[\/latex] \u2192 +<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 18.5592%;\">[latex](5-4)[\/latex] \u2192 +<\/td>\n<td class=\"border-t-border-100\/50 [&amp;:not(:first-child)]:-x-[hsla(var(--border-100) \/ 0.5)] border-t-[0.5px] px-2 [&amp;:not(:first-child)]:border-l-[0.5px]\" style=\"width: 16.0654%;\">(+)(+)(+) = +<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm311019\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=311019&theme=lumen&iframe_resize_id=ohm311019&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":13,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":74,"module-header":"- Select Header 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