Factor. 2u^2 + 9u + 9 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2u^2 + 9u + 9 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 9Find factorable numbers: Find two numbers that multiply to ac (a times c) and add up to b. In this case, ac = 2 * 9 = 18, and we need two numbers that multiply to 18 and add up to 9.Rewrite middle term: The two numbers that satisfy the conditions are 3 and 6 because 3 * 6 = 18 and 3 + 6 = 9.Group terms for factoring: Rewrite the middle term 9u using the two numbers found in the previous step. This will allow us to split the middle term for factoring by grouping. 2u^2 + 9u + 9 becomes 2u^2 + 3u + 6u + 9.Factor out common factors: Group the terms into two pairs and factor out the common factor from each pair. From 2u^2 + 3u, factor out u to get u(2u + 3). From 6u + 9, factor out 3 to get 3(2u + 3).Final factored form: Notice that both groups now have a common binomial factor (2u + 3). Factor out the common binomial factor. The factored form is (u + 3)(2u + 3).

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Factor. $\newline$ $2u^2 + 9u + 9$

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

\newline

2u^2 + 9u + 9

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2u^2 + 9u + 9$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 9$
Find factorable numbers: Find two numbers that multiply to $ac$ ( $a \times c$ ) and add up to $b$ . In this case, $ac = 2 \times 9 = 18$ , and we need two numbers that multiply to $18$ and add up to $9$ .
Rewrite middle term: The two numbers that satisfy the conditions are $3$ and $6$ because $3 \times 6 = 18$ and $3 + 6 = 9$ .
Group terms for factoring: Rewrite the middle term $9u$ using the two numbers found in the previous step. This will allow us to split the middle term for factoring by grouping. $\newline$ $2u^2 + 9u + 9$ becomes $2u^2 + 3u + 6u + 9$ .
Factor out common factors: Group the terms into two pairs and factor out the common factor from each pair. $\newline$ From $2u^2 + 3u$ , factor out $u$ to get $u(2u + 3)$ . $\newline$ From $6u + 9$ , factor out $3$ to get $3(2u + 3)$ .
Final factored form: Notice that both groups now have a common binomial factor $2u + 3$ . Factor out the common binomial factor. $\newline$ The factored form is $u + 3$ $2u + 3$ .