Factor. 2s^2 + 7s + 6 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2s^2 + 7s + 6 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 7, c = 6Find two numbers: Find two numbers that multiply to a*c (2*6 = 12) and add up to b (7). The numbers 3 and 4 multiply to 12 and add up to 7.Rewrite middle term: Rewrite the middle term 7s using the two numbers found in the previous step: 3s and 4s. 2s^2 + 7s + 6 can be expressed as 2s^2 + 3s + 4s + 6.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2s^2 + 3s) + (4s + 6)Factor out common factor: Factor out the greatest common factor from each group. s(2s + 3) + 2(2s + 3)Final factored form: Since both groups contain the common factor (2s + 3), factor it out. (s + 2)(2s + 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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2s^2 + 7s + 6

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2s^2 + 7s + 6$ by comparing it to the standard form $ax^2 + bx + c$ . $\newline$ $a = 2$ , $b = 7$ , $c = 6$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*6 = 12$ ) and add up to $b$ ( $7$ ). $\newline$ The numbers $3$ and $4$ multiply to $12$ and add up to $7$ .
Rewrite middle term: Rewrite the middle term $7s$ using the two numbers found in the previous step: $3s$ and $4s$ . $2s^2 + 7s + 6$ can be expressed as $2s^2 + 3s + 4s + 6$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(2s^2 + 3s) + (4s + 6)$
Factor out common factor: Factor out the greatest common factor from each group. $s(2s + 3) + 2(2s + 3)$
Final factored form: Since both groups contain the common factor $(2s + 3)$ , factor it out. $(s + 2)(2s + 3)$ is the factored form of the quadratic expression.