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Factor. $\newline$ $2x^2 - 7x + 5$

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Factor polynomials

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Q. Factor.

\newline

2x^2 - 7x + 5

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2x^2 - 7x + 5$ . Compare $2x^2 - 7x + 5$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find Product and Sum: Find two numbers whose product is $a*c$ ( $2*5 = 10$ ) and whose sum is $b$ ( $-7$ ). $\newline$ We need to find two numbers that multiply to $10$ and add up to $-7$ . $\newline$ The numbers $-2$ and $-5$ work because: $\newline$ $-2 * -5 = 10$ $\newline$ $-2 + -5 = -7$
Rewrite Middle Term: Rewrite the middle term $-7x$ using the two numbers found in Step $2$ . $\newline$ $2x^2 - 7x + 5$ can be rewritten as $2x^2 - 2x - 5x + 5$ .
Factor by Grouping: Factor by grouping. $\newline$ Group the terms: $(2x^2 - 2x) + (-5x + 5)$ . $\newline$ Factor out the common factors from each group. $\newline$ $2x(x - 1) - 5(x - 1)$ .
Factor out Common Factor: Factor out the common binomial factor $(x - 1)$ . $(2x - 5)(x - 1)$ is the factored form.

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