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

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 9w^2 + 11w + 2 by comparing it to the standard form ax^2 + bx + c. a = 9, b = 11, c = 2Find two numbers: Find two numbers that multiply to a*c (9*2 = 18) and add up to b (11). The numbers that satisfy these conditions are 9 and 2 because 9*2 = 18 and 9+2 = 11.Rewrite middle term: Rewrite the middle term 11w using the two numbers found in the previous step. 9w^2 + 11w + 2 can be rewritten as 9w^2 + 9w + 2w + 2.Group terms: Group the terms into two pairs: (9w^2 + 9w) and (2w + 2).Factor out common factor: Factor out the greatest common factor from each pair. From the first pair (9w^2 + 9w), factor out 9w to get 9w(w + 1). From the second pair (2w + 2), factor out 2 to get 2(w + 1).Write factored form: Notice that both groups now have a common factor of (w + 1). Write the expression as the product of this common factor and the factors found in the previous step. The factored form is (9w + 2)(w + 1).

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Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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9w^2 + 11w + 2

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $9w^2 + 11w + 2$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 9$ , $b = 11$ , $c = 2$
Find two numbers: Find two numbers that multiply to $a*c$ ( $9*2 = 18$ ) and add up to $b$ ( $11$ ). $\newline$ The numbers that satisfy these conditions are $9$ and $2$ because $9*2 = 18$ and $9+2 = 11$ .
Rewrite middle term: Rewrite the middle term $11w$ using the two numbers found in the previous step. $\newline$ $9w^2 + 11w + 2$ can be rewritten as $9w^2 + 9w + 2w + 2$ .
Group terms: Group the terms into two pairs: $9w^2 + 9w$ and $2w + 2$ .
Factor out common factor: Factor out the greatest common factor from each pair. $\newline$ From the first pair $9w^2 + 9w$ , factor out $9w$ to get $9w(w + 1)$ . $\newline$ From the second pair $2w + 2$ , factor out $2$ to get $2(w + 1)$ .
Write factored form: Notice that both groups now have a common factor of $(w + 1)$ . $\newline$ Write the expression as the product of this common factor and the factors found in the previous step. $\newline$ The factored form is $(9w + 2)(w + 1)$ .