Factor. 2h^2 + 9h + 9 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2h^2 + 9h + 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). We are looking for two numbers that multiply to 18 and add up to 9. The numbers 6 and 3 satisfy these conditions because 6*3 = 18 and 6+3 = 9.Rewrite middle term: Rewrite the middle term 9h using the two numbers found in the previous step. This will allow us to split the middle term for factoring by grouping. 2h^2 + 9h + 9 can be rewritten as 2h^2 + 6h + 3h + 9.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together, then factor out the common factor from each group. From 2h^2 + 6h, we can factor out 2h to get 2h(h + 3). From 3h + 9, we can factor out 3 to get 3(h + 3). Now we have 2h(h + 3) + 3(h + 3).Factor out common factor: Factor out the common binomial factor (h + 3) from both groups. The expression becomes (2h + 3)(h + 3).

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

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

\newline

2h^2 + 9h + 9

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2h^2 + 9h + 9$ 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 $b$ ( $9$ ). We are looking for two numbers that multiply to $18$ and add up to $9$ . The numbers $6$ and $3$ satisfy these conditions because $6*3 = 18$ and $6+3 = 9$ .
Rewrite middle term: Rewrite the middle term $9h$ using the two numbers found in the previous step. This will allow us to split the middle term for factoring by grouping. $\newline$ $2h^2 + 9h + 9$ can be rewritten as $2h^2 + 6h + 3h + 9$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together, then factor out the common factor from each group. $\newline$ From $2h^2 + 6h$ , we can factor out $2h$ to get $2h(h + 3)$ . $\newline$ From $3h + 9$ , we can factor out $3$ to get $3(h + 3)$ . $\newline$ Now we have $2h(h + 3) + 3(h + 3)$ .
Factor out common factor: Factor out the common binomial factor $(h + 3)$ from both groups. $\newline$ The expression becomes $(2h + 3)(h + 3)$ .