Factor. 3g^2 + 10g + 7 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 3g^2 + 10g + 7 by comparing it with the standard form ax^2 + bx + c. a = 3 b = 10 c = 7Find two numbers: Find two numbers that multiply to a*c (3*7=21) and add up to b (10). The numbers that satisfy these conditions are 3 and 7 because 3*7 = 21 and 3+7 = 10.Rewrite middle term: Rewrite the middle term, 10g, using the two numbers found in the previous step. 3g^2 + 10g + 7 can be rewritten as 3g^2 + 3g + 7g + 7.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (3g^2 + 3g) + (7g + 7) Factor out the greatest common factor from each group. g(3g + 3) + 7(3g + 3)Notice common factor: Notice that (3g + 3) is a common factor in both groups. Factor out (3g + 3) from the expression. (3g + 3)(g + 7)Check factored form: Check the factored form by expanding it to ensure it equals the original expression. (3g + 3)(g + 7) = 3g^2 + 21g + 3g + 21 = 3g^2 + 24g + 21 This is not equal to the original expression, which means there is a math error.

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Factor. $\newline$ $3g^2 + 10g + 7$

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

\newline

3g^2 + 10g + 7

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3g^2 + 10g + 7$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 3$ $\newline$ $b = 10$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ ( $3*7=21$ ) and add up to $b$ ( $10$ ). $\newline$ The numbers that satisfy these conditions are $3$ and $7$ because $3*7 = 21$ and $3+7 = 10$ .
Rewrite middle term: Rewrite the middle term, $10g$ , using the two numbers found in the previous step. $\newline$ $3g^2 + 10g + 7$ can be rewritten as $3g^2 + 3g + 7g + 7$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(3g^2 + 3g) + (7g + 7)$ $\newline$ Factor out the greatest common factor from each group. $\newline$ $g(3g + 3) + 7(3g + 3)$
Notice common factor: Notice that $(3g + 3)$ is a common factor in both groups. $\newline$ Factor out $(3g + 3)$ from the expression. $\newline$ $(3g + 3)(g + 7)$
Check factored form: Check the factored form by expanding it to ensure it equals the original expression. $\newline$ $(3g + 3)(g + 7) = 3g^2 + 21g + 3g + 21 = 3g^2 + 24g + 21$ $\newline$ This is not equal to the original expression, which means there is a math error.