Factor. 2g^2 + 9g + 10 ______

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2g^2 + 9g + 10 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 10Find two numbers: Find two numbers that multiply to a*c (2*10 = 20) and add up to b (9). The numbers 5 and 4 multiply to 20 and add up to 9.Rewrite middle term: Rewrite the middle term 9g using the two numbers found in the previous step: 5g and 4g. The expression becomes 2g^2 + 5g + 4g + 10.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms separately. (2g^2 + 5g) + (4g + 10)Factor out common factor: Factor out the greatest common factor from each group. g(2g + 5) + 2(2g + 5)Final factorization: Since both groups contain the common factor (2g + 5), factor it out. (g + 2)(2g + 5)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2g^2 + 9g + 10

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2g^2 + 9g + 10$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 10$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*10 = 20$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers $5$ and $4$ multiply to $20$ and add up to $9$ .
Rewrite middle term: Rewrite the middle term $9g$ using the two numbers found in the previous step: $5g$ and $4g$ . The expression becomes $2g^2 + 5g + 4g + 10$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms separately. $\newline$ $(2g^2 + 5g) + (4g + 10)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $g(2g + 5) + 2(2g + 5)$
Final factorization: Since both groups contain the common factor $(2g + 5)$ , factor it out. $(g + 2)(2g + 5)$