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

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Factor quadratics with other leading coefficients

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Q. Factor.

\newline

5x^2 + 7x + 2

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $5x^2 + 7x + 2$ . Compare $5x^2 + 7x + 2$ with $ax^2 + bx + c$ . $a = 5$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $5*2=10$ ) and add up to $b$ (which is $7$ ). $\newline$ The two numbers that satisfy these conditions are $5$ and $2$ because: $\newline$ $5 * 2 = 10$ $\newline$ $5 + 2 = 7$
Rewrite middle term: Rewrite the middle term, $7x$ , using the two numbers found in Step $2$ . $\newline$ $5x^2 + 7x + 2$ can be rewritten as $5x^2 + 5x + 2x + 2$ .
Factor by grouping: Factor by grouping. $\newline$ Group the first two terms and the last two terms: $\newline$ $(5x^2 + 5x) + (2x + 2)$ $\newline$ Factor out the common factor from each group: $\newline$ $5x(x + 1) + 2(x + 1)$
Factor out common binomial: Factor out the common binomial factor, which is $(x + 1)$ . The factored form is $(5x + 2)(x + 1)$ .

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