Factor. 4g^2 + 9g + 5 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 4g^2 + 9g + 5 by comparing it to the standard form ax^2 + bx + c. a = 4, b = 9, c = 5Find two numbers: Find two numbers that multiply to a*c (4*5 = 20) and add up to b (9). The numbers that satisfy these conditions are 4 and 5 because 4*5 = 20 and 4+5 = 9.Rewrite middle term: Rewrite the middle term 9g using the two numbers found in the previous step. 4g^2 + 9g + 5 can be rewritten as 4g^2 + 4g + 5g + 5.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (4g^2 + 4g) + (5g + 5)Factor out common factor: Factor out the common factor from each group. 4g(g + 1) + 5(g + 1)Factor out common factor: Since both groups contain the common factor (g + 1), factor this out. (4g + 5)(g + 1)

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Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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4g^2 + 9g + 5

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $4g^2 + 9g + 5$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 4$ , $b = 9$ , $c = 5$
Find two numbers: Find two numbers that multiply to $a*c$ ( $4*5 = 20$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers that satisfy these conditions are $4$ and $5$ because $4*5 = 20$ and $4+5 = 9$ .
Rewrite middle term: Rewrite the middle term $9g$ using the two numbers found in the previous step. $4g^2 + 9g + 5$ can be rewritten as $4g^2 + 4g + 5g + 5$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(4g^2 + 4g) + (5g + 5)$
Factor out common factor: Factor out the common factor from each group. $4g(g + 1) + 5(g + 1)$
Factor out common factor: Since both groups contain the common factor $(g + 1)$ , factor this out. $(4g + 5)(g + 1)$