Factor. 2p^2 + 9p + 7 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2p^2 + 9p + 7 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 7Find two numbers: Find two numbers that multiply to a*c (2*7 = 14) and add up to b (9). The numbers that satisfy these conditions are 2 and 7 because 2*7 = 14 and 2+7 = 9.Rewrite middle term: Rewrite the middle term 9p using the two numbers found in the previous step. 2p^2 + 9p + 7 can be rewritten as 2p^2 + 2p + 7p + 7.Factor by grouping: Factor by grouping. Group the terms into two pairs and factor out the common factor from each pair. From the first pair 2p^2 + 2p, factor out 2p to get 2p(p + 1). From the second pair 7p + 7, factor out 7 to get 7(p + 1).Factor out common binomial: Now that we have 2p(p + 1) + 7(p + 1), we can factor out the common binomial factor (p + 1). The factored form is (2p + 7)(p + 1).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2p^2 + 9p + 7

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2p^2 + 9p + 7$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 7$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*7 = 14$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers that satisfy these conditions are $2$ and $7$ because $2*7 = 14$ and $2+7 = 9$ .
Rewrite middle term: Rewrite the middle term $9p$ using the two numbers found in the previous step. $\newline$ $2p^2 + 9p + 7$ can be rewritten as $2p^2 + 2p + 7p + 7$ .
Factor by grouping: Factor by grouping. Group the terms into two pairs and factor out the common factor from each pair. $\newline$ From the first pair $2p^2 + 2p$ , factor out $2p$ to get $2p(p + 1)$ . $\newline$ From the second pair $7p + 7$ , factor out $7$ to get $7(p + 1)$ .
Factor out common binomial: Now that we have $2p(p + 1) + 7(p + 1)$ , we can factor out the common binomial factor $(p + 1)$ . The factored form is $(2p + 7)(p + 1)$ .