Factor. 2w^2 + 11w + 9 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2w^2 + 11w + 9 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 11, c = 9Find suitable numbers: Find two numbers that multiply to a*c (2*9 = 18) and add up to b (11). The numbers 2 and 9 satisfy these conditions because 2*9 = 18 and 2+9 = 11.Rewrite middle term: Rewrite the middle term 11w using the two numbers found in the previous step. 2w^2 + 11w + 9 can be rewritten as 2w^2 + 2w + 9w + 9.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (2w^2 + 2w) + (9w + 9)Factor out common factor: Factor out the greatest common factor from each group. 2w(w + 1) + 9(w + 1)Final factorization: Since both groups contain the common factor (w + 1), factor this out. (2w + 9)(w + 1)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2w^2 + 11w + 9

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2w^2 + 11w + 9$ by comparing it to the standard form $ax^2 + bx + c$ .
$a = 2$ , $b = 11$ , $c = 9$
Find suitable numbers: Find two numbers that multiply to $a*c$ ( $2*9 = 18$ ) and add up to $b$ ( $11$ ). $\newline$ The numbers $2$ and $9$ satisfy these conditions because $2*9 = 18$ and $2+9 = 11$ .
Rewrite middle term: Rewrite the middle term $11w$ using the two numbers found in the previous step. $\newline$ $2w^2 + 11w + 9$ can be rewritten as $2w^2 + 2w + 9w + 9$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(2w^2 + 2w) + (9w + 9)$
Factor out common factor: Factor out the greatest common factor from each group. $2w(w + 1) + 9(w + 1)$
Final factorization: Since both groups contain the common factor $(w + 1)$ , factor this out. $(2w + 9)(w + 1)$