Factor. x^(2)-13 x+40 Answer:

Identify Quadratic Equation: Identify the quadratic equation to be factored. The given quadratic equation is x^2 - 13x + 40. We need to find two numbers that multiply to give the constant term (40) and add up to give the coefficient of the linear term (-13).Find Multiplying Numbers: Find two numbers that multiply to 40 and add up to -13. The numbers that satisfy these conditions are -8 and -5 because (-8) * (-5) = 40 and (-8) + (-5) = -13.Write Factored Form: Write the quadratic equation in its factored form using the two numbers found in Step 2. The factored form of the quadratic equation is (x - 8)(x - 5).Check Factored Form: Check the factored form by expanding it to ensure it matches the original quadratic equation. Expanding (x - 8)(x - 5) gives x^2 - 5x - 8x + 40, which simplifies to x^2 - 13x + 40. This matches the original quadratic equation, so the factoring is correct.

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Factor. $\newline$ $x^{2}-13 x+40$ $\newline$ Answer:

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Algebra 2

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Q. Factor.

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x^{2}-13 x+40

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Answer:

Identify Quadratic Equation: Identify the quadratic equation to be factored. $\newline$ The given quadratic equation is $x^2 - 13x + 40$ . $\newline$ We need to find two numbers that multiply to give the constant term $(40)$ and add up to give the coefficient of the linear term $(-13)$ .
Find Multiplying Numbers: Find two numbers that multiply to $40$ and add up to $-13$ . The numbers that satisfy these conditions are $-8$ and $-5$ because $(-8) \times (-5) = 40$ and $(-8) + (-5) = -13$ .
Write Factored Form: Write the quadratic equation in its factored form using the two numbers found in Step $2$ . $\newline$ The factored form of the quadratic equation is $(x - 8)(x - 5)$ .
Check Factored Form: Check the factored form by expanding it to ensure it matches the original quadratic equation. $\newline$ Expanding $(x - 8)(x - 5)$ gives $x^2 - 5x - 8x + 40$ , which simplifies to $x^2 - 13x + 40$ . $\newline$ This matches the original quadratic equation, so the factoring is correct.