Factor. 2j^2 + 9j + 9 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2j^2 + 9j + 9 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 9Find two numbers: Find two numbers that multiply to a*c (2*9 = 18) and add up to b (9). The two numbers that satisfy these conditions are 3 and 6, since 3*6 = 18 and 3+6 = 9.Rewrite middle term: Rewrite the middle term 9j using the two numbers found in the previous step. 2j^2 + 9j + 9 can be rewritten as 2j^2 + 3j + 6j + 9.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2j^2 + 3j) + (6j + 9)Factor out common factor: Factor out the greatest common factor from each group. j(2j + 3) + 3(2j + 3)Final factored form: Since both groups contain the common factor (2j + 3), factor this out. (j + 3)(2j + 3) is the factored form of the quadratic expression.

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2j^2 + 9j + 9

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2j^2 + 9j + 9$ by comparing it to the standard form $ax^2 + bx + c$ .
$a = 2$ , $b = 9$ , $c = 9$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*9 = 18$ ) and add up to $b$ ( $9$ ). $\newline$ The two numbers that satisfy these conditions are $3$ and $6$ , since $3*6 = 18$ and $3+6 = 9$ .
Rewrite middle term: Rewrite the middle term $9j$ using the two numbers found in the previous step. $\newline$ $2j^2 + 9j + 9$ can be rewritten as $2j^2 + 3j + 6j + 9$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(2j^2 + 3j) + (6j + 9)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $j(2j + 3) + 3(2j + 3)$
Final factored form: Since both groups contain the common factor $(2j + 3)$ , factor this out. $(j + 3)(2j + 3)$ is the factored form of the quadratic expression.