Factor completely. 2x^(2)-40 x+200=

Find Common Factor: Look for a common factor in all terms. The terms 2x^2, -40x, and 200 all have a common factor of 2. Factor out the 2: 2(x^2 - 20x + 100).Factor Quadratic Expression: Now, factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to 100 and add up to -20. The numbers -10 and -10 satisfy these conditions. So, we can write x^2 - 20x + 100 as (x - 10)(x - 10) or (x - 10)^2.Combine Factors: Combine the factored quadratic with the common factor. The complete factorization is 2(x - 10)^2.

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Factor completely. $\newline$ $2x^{2}-40x+200=$

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor completely.

\newline

2x^{2}-40x+200=

Find Common Factor: Look for a common factor in all terms. $\newline$ The terms $2x^2$ , $-40x$ , and $200$ all have a common factor of $2$ . $\newline$ Factor out the $2$ : $2(x^2 - 20x + 100)$ .
Factor Quadratic Expression: Now, factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $100$ and add up to $-20$ . $\newline$ The numbers $-10$ and $-10$ satisfy these conditions. $\newline$ So, we can write $x^2 - 20x + 100$ as $(x - 10)(x - 10)$ or $(x - 10)^2$ .
Combine Factors: Combine the factored quadratic with the common factor. $\newline$ The complete factorization is $2(x - 10)^2$ .