Factor. 9x^2 - 24x + 16 ______

Check Factoring Possibility: Determine if the quadratic can be factored using the form (ax)^2 - 2abx + b^2 = (ax - b)^2. The given quadratic is 9x^2 - 24x + 16. We need to check if there are numbers a and b such that (ax)^2 = 9x^2, -2abx = -24x, and b^2 = 16.Find a and b: Find the values of a and b. For (ax)^2 = 9x^2, we have a = 3 because (3x)^2 = 9x^2. For b^2 = 16, we have b = 4 because 4^2 = 16. Now we check if -2abx = -24x with a = 3 and b = 4. -2 * 3 * 4 * x = -24x, which is true.Write Factored Form: Write the factored form using the values of a and b. The factored form is (ax - b)^2 = (3x - 4)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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9x^2 - 24x + 16

Check Factoring Possibility: Determine if the quadratic can be factored using the form $(ax)^2 - 2abx + b^2 = (ax - b)^2$ . $\newline$ The given quadratic is $9x^2 - 24x + 16$ . We need to check if there are numbers $a$ and $b$ such that $(ax)^2 = 9x^2$ , $-2abx = -24x$ , and $b^2 = 16$ .
Find a and b: Find the values of a and b. $\newline$ For $(ax)^2 = 9x^2$ , we have $a = 3$ because $(3x)^2 = 9x^2$ . $\newline$ For $b^2 = 16$ , we have $b = 4$ because $4^2 = 16$ . $\newline$ Now we check if $-2abx = -24x$ with $a = 3$ and $b = 4$ . $\newline$ $-2 \times 3 \times 4 \times x = -24x$ , which is true.
Write Factored Form: Write the factored form using the values of $a$ and $b$ . The factored form is $(ax - b)^2 = (3x - 4)^2$ .