Factor. 2z^2 + 9z + 7 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2z^2 + 9z + 7 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 9, c = 7.Find suitable numbers: Find two numbers that multiply to a*c (2*7 = 14) and add up to b (9). The numbers that satisfy these conditions are 2 and 7 because 2*7 = 14 and 2+7 = 9.Rewrite middle term: Rewrite the middle term, 9z, using the two numbers found in the previous step: 2z and 7z. The expression becomes 2z^2 + 2z + 7z + 7.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2z^2 + 2z) + (7z + 7).Factor out common factor: Factor out the greatest common factor from each group. 2z(z + 1) + 7(z + 1).Final factored form: Since both groups contain the common factor (z + 1), factor it out. The factored form is (2z + 7)(z + 1).

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2z^2 + 9z + 7

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2z^2 + 9z + 7$ by comparing it to the standard form $ax^2 + bx + c$ . $a = 2$ , $b = 9$ , $c = 7$ .
Find suitable numbers: Find two numbers that multiply to $a*c$ ( $2*7 = 14$ ) and add up to $b$ ( $9$ ). $\newline$ The numbers that satisfy these conditions are $2$ and $7$ because $2*7 = 14$ and $2+7 = 9$ .
Rewrite middle term: Rewrite the middle term, $9z$ , using the two numbers found in the previous step: $2z$ and $7z$ . The expression becomes $2z^2 + 2z + 7z + 7$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $2z^2 + 2z$ + $7z + 7$ .
Factor out common factor: Factor out the greatest common factor from each group. $2z(z + 1) + 7(z + 1)$ .
Final factored form: Since both groups contain the common factor $(z + 1)$ , factor it out. $\newline$ The factored form is $(2z + 7)(z + 1)$ .