Problem of the Week

Updated at May 30, 2022 9:40 AM

This week's problem comes from the algebra category.

How would you find the factors of \(20{z}^{2}+6z-2\)?

Let's begin!



\[20{z}^{2}+6z-2\]

1
Find the Greatest Common Factor (GCF).
GCF = \(2\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[2(\frac{20{z}^{2}}{2}+\frac{6z}{2}-\frac{2}{2})\]

3
Simplify each term in parentheses.
\[2(10{z}^{2}+3z-1)\]

4
Split the second term in \(10{z}^{2}+3z-1\) into two terms.
\[2(10{z}^{2}+5z-2z-1)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(5z(2z+1)-(2z+1))\]

6
Factor out the common term \(2z+1\).
\[2(2z+1)(5z-1)\]

Done
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