Factor. 2g^2 + 7g + 5 ____

Identify a, b, c: Identify a, b, and c in the quadratic expression 2g^2 + 7g + 5 by comparing it with the standard form ax^2 + bx + c. a = 2 b = 7 c = 5Find two numbers: Find two numbers that multiply to a*c (which is 2*5=10) and add up to b (which is 7). The two numbers that satisfy these conditions are 2 and 5 because: 2 * 5 = 10 2 + 5 = 7Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step 2. 2g^2 + 7g + 5 can be rewritten as 2g^2 + 2g + 5g + 5 by splitting the middle term.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (2g^2 + 2g) + (5g + 5) Now, factor out the common factors from each group. 2g(g + 1) + 5(g + 1)Factor out common binomial: Factor out the common binomial factor (g + 1). The factored form of the expression is (2g + 5)(g + 1).

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2g^2 + 7g + 5

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2g^2 + 7g + 5$ by comparing it with the standard form $ax^2 + bx + c$ . $\newline$ $a = 2$ $\newline$ $b = 7$ $\newline$ $b$ $0$
Find two numbers: Find two numbers that multiply to $a*c$ (which is $2*5=10$ ) and add up to $b$ (which is $7$ ). $\newline$ The two numbers that satisfy these conditions are $2$ and $5$ because: $\newline$ $2 \times 5 = 10$ $\newline$ $2 + 5 = 7$
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found in Step $2$ . $\newline$ $2g^2 + 7g + 5$ can be rewritten as $2g^2 + 2g + 5g + 5$ by splitting the middle term.
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $\newline$ $(2g^2 + 2g) + (5g + 5)$ $\newline$ Now, factor out the common factors from each group. $\newline$ $2g(g + 1) + 5(g + 1)$
Factor out common binomial: Factor out the common binomial factor $(g + 1)$ . $\newline$ The factored form of the expression is $(2g + 5)(g + 1)$ .