Factor. 4g^2 + 7g + 3 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 4g^2 + 7g + 3 by comparing it with the standard form ax^2 + bx + c. a = 4 b = 7 c = 3Find Numbers Multiply Add: Find two numbers that multiply to a*c (which is 4*3=12) and add up to b (which is 7). The numbers that satisfy these conditions are 4 and 3 because: 4 * 3 = 12 4 + 3 = 7Rewrite Middle Term: Rewrite the middle term, 7g, using the two numbers found in the previous step. 4g^2 + 7g + 3 can be rewritten as 4g^2 + 4g + 3g + 3.Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. (4g^2 + 4g) + (3g + 3)Factor out Common Factor: Factor out the common factor from each group. 4g(g + 1) + 3(g + 1)Factor Out Groups: Since both groups contain the common factor (g + 1), factor this out. (4g + 3)(g + 1)

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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4g^2 + 7g + 3

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $4g^2 + 7g + 3$ by comparing it with the standard form $ax^2 + bx + c$ .
$a = 4$
$b = 7$
$b$ $0$
Find Numbers Multiply Add: Find two numbers that multiply to $a*c$ (which is $4*3=12$ ) and add up to $b$ (which is $7$ ). $\newline$ The numbers that satisfy these conditions are $4$ and $3$ because: $\newline$ $4 \times 3 = 12$ $\newline$ $4 + 3 = 7$
Rewrite Middle Term: Rewrite the middle term, $7g$ , using the two numbers found in the previous step. $\newline$ $4g^2 + 7g + 3$ can be rewritten as $4g^2 + 4g + 3g + 3$ .
Factor by Grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(4g^2 + 4g) + (3g + 3)$
Factor out Common Factor: Factor out the common factor from each group. $4g(g + 1) + 3(g + 1)$
Factor Out Groups: Since both groups contain the common factor $(g + 1)$ , factor this out. $(4g + 3)(g + 1)$