Factor. 2h^2 + 15h + 7 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2h^2 + 15h + 7 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 15, c = 7Find two numbers: Find two numbers that multiply to a*c (2*7 = 14) and add up to b (15). The numbers that satisfy these conditions are 14 and 1 because 14*1 = 14 and 14+1 = 15.Rewrite middle term: Rewrite the middle term, 15h, using the two numbers found in the previous step: 14h and 1h. The expression becomes 2h^2 + 14h + 1h + 7.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2h^2 + 14h) + (1h + 7)Factor out common factor: Factor out the greatest common factor from each group. 2h(h + 7) + 1(h + 7)Since both groups contain the common factor (h + 7), factor it out. (2h + 1)(h + 7)

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Algebra 1

Factor quadratics with other leading coefficients

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Q. Factor.

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2h^2 + 15h + 7

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2h^2 + 15h + 7$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 15$ , $c = 7$
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*7 = 14$ ) and add up to $b$ ( $15$ ). $\newline$ The numbers that satisfy these conditions are $14$ and $1$ because $14*1 = 14$ and $14+1 = 15$ .
Rewrite middle term: Rewrite the middle term, $15h$ , using the two numbers found in the previous step: $14h$ and $1h$ . The expression becomes $2h^2 + 14h + 1h + 7$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(2h^2 + 14h) + (1h + 7)$
Factor out common factor: Factor out the greatest common factor from each group. $2h(h + 7) + 1(h + 7)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $2h(h + 7) + 1(h + 7)$ Since both groups contain the common factor $(h + 7)$ , factor it out. $\newline$ $(2h + 1)(h + 7)$