Factor. 2s^2 + 9s + 9 ____

Identify Variables: Identify a, b, and c in the quadratic expression 2s^2 + 9s + 9 by comparing it with the standard form ax^2 + bx + c. a = 2 b = 9 c = 9Find Multiplying Numbers: Find two numbers that multiply to a*c (which is 2*9=18) and add up to b (which is 9). We need to find 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 of the quadratic expression using the two numbers found in Step 2. 2s^2 + 9s + 9 can be rewritten as 2s^2 + 6s + 3s + 9 by splitting the middle term into 6s and 3s.Factor by Grouping: Factor by grouping. Group the terms into two pairs and factor out the common factor from each pair. First pair: 2s^2 + 6s can be factored as 2s(s + 3). Second pair: 3s + 9 can be factored as 3(s + 3).Write Factored Form: Write the factored form of the expression by factoring out the common binomial (s + 3). The expression becomes (2s + 3)(s + 3) after factoring out the common binomial.

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2s^2 + 9s + 9

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $2s^2 + 9s + 9$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 2$
$b = 9$
$c = 9$
Find Multiplying Numbers: Find two numbers that multiply to $a*c$ (which is $2*9=18$ ) and add up to $b$ (which is $9$ ). $\newline$ We need to find 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 of the quadratic expression using the two numbers found in Step $2$ . $\newline$ $2s^2 + 9s + 9$ can be rewritten as $2s^2 + 6s + 3s + 9$ by splitting the middle term into $6s$ and $3s$ .
Factor by Grouping: Factor by grouping. Group the terms into two pairs and factor out the common factor from each pair. $\newline$ First pair: $2s^2 + 6s$ can be factored as $2s(s + 3)$ . $\newline$ Second pair: $3s + 9$ can be factored as $3(s + 3)$ .
Write Factored Form: Write the factored form of the expression by factoring out the common binomial $(s + 3)$ . The expression becomes $(2s + 3)(s + 3)$ after factoring out the common binomial.