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

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

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Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2q^2 + 11q + 9

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