Factor. 2z^2 + 13z + 11 ______

Identify Coefficients: Identify the coefficients of the quadratic expression. The quadratic expression is in the form az^2 + bz + c, where a, b, and c are constants. For the expression 2z^2 + 13z + 11, we have: a = 2 b = 13 c = 11Find Multiplying Numbers: Find two numbers that multiply to ac (a times c) and add up to b. We need to find two numbers that multiply to (2)(11) = 22 and add up to 13. The numbers that satisfy these conditions are 2 and 11 because: 2 * 11 = 22 2 + 11 = 13Rewrite Middle Term: Rewrite the middle term using the two numbers found in the previous step. We can express the middle term 13z as the sum of 2z and 11z. This gives us: 2z^2 + 13z + 11 = 2z^2 + 2z + 11z + 11Factor by Grouping: Factor by grouping. We group the terms as follows: (2z^2 + 2z) + (11z + 11) Now we factor out the common factors from each group: 2z(z + 1) + 11(z + 1)Factor out Binomial: Factor out the common binomial. We notice that (z + 1) is common in both terms, so we factor it out: 2z(z + 1) + 11(z + 1) = (2z + 11)(z + 1)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor. $\newline$ $2z^2 + 13z + 11$

View step-by-step help

Home

Math Problems

Algebra 1

Factor quadratics with other leading coefficients

Full solution

Q. Factor.

\newline

2z^2 + 13z + 11

Identify Coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is in the form $az^2 + bz + c$ , where $a$ , $b$ , and $c$ are constants. For the expression $2z^2 + 13z + 11$ , we have: $\newline$ $a = 2$ $\newline$ $b = 13$ $\newline$ $c = 11$
Find Multiplying Numbers: Find two numbers that multiply to $ac$ ( $a$ times $c$ ) and add up to $b$ . We need to find two numbers that multiply to $(2)(11) = 22$ and add up to $13$ . The numbers that satisfy these conditions are $2$ and $11$ because: $2 \times 11 = 22$ $2 + 11 = 13$
Rewrite Middle Term: Rewrite the middle term using the two numbers found in the previous step. $\newline$ We can express the middle term $13z$ as the sum of $2z$ and $11z$ . This gives us: $\newline$ $2z^2 + 13z + 11 = 2z^2 + 2z + 11z + 11$
Factor by Grouping: Factor by grouping. $\newline$ We group the terms as follows: $\newline$ $(2z^2 + 2z) + (11z + 11)$ $\newline$ Now we factor out the common factors from each group: $\newline$ $2z(z + 1) + 11(z + 1)$
Factor out Binomial: Factor out the common binomial. $\newline$ We notice that $(z + 1)$ is common in both terms, so we factor it out: $\newline$ $2z(z + 1) + 11(z + 1) = (2z + 11)(z + 1)$