Factor. 2z^2 + 5z + 3 ____

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression 2z^2 + 5z + 3 by comparing it to the standard form ax^2 + bx + c. a = 2, b = 5, c = 3.Find two numbers: Find two numbers that multiply to a*c (2*3 = 6) and add up to b (5). The numbers 2 and 3 multiply to 6 and add up to 5.Rewrite middle term: Rewrite the middle term 5z using the two numbers found in the previous step. 2z^2 + 5z + 3 can be rewritten as 2z^2 + 2z + 3z + 3.Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. (2z^2 + 2z) + (3z + 3).Factor out common factor: Factor out the greatest common factor from each group. 2z(z + 1) + 3(z + 1).Factor out (z + 1): Since both groups contain the factor (z + 1), factor this out. (2z + 3)(z + 1) is the factored form of 2z^2 + 5z + 3.

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Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

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2z^2 + 5z + 3

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $2z^2 + 5z + 3$ by comparing it to the standard form $ax^2 + bx + c$ .
$a = 2$ , $b = 5$ , $c = 3$ .
Find two numbers: Find two numbers that multiply to $a*c$ ( $2*3 = 6$ ) and add up to $b$ ( $5$ ). $\newline$ The numbers $2$ and $3$ multiply to $6$ and add up to $5$ .
Rewrite middle term: Rewrite the middle term $5z$ using the two numbers found in the previous step. $\newline$ $2z^2 + 5z + 3$ can be rewritten as $2z^2 + 2z + 3z + 3$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms. $\newline$ $(2z^2 + 2z) + (3z + 3)$ .
Factor out common factor: Factor out the greatest common factor from each group. $2z(z + 1) + 3(z + 1)$ .
Factor out $(z + 1)$ : Since both groups contain the factor $(z + 1)$ , factor this out. $(2z + 3)(z + 1)$ is the factored form of $2z^2 + 5z + 3$ .