Problem of the Week

Updated at May 24, 2021 12:47 PM

How can we compute the factors of \(4{z}^{2}+6z-4\)?

Below is the solution.



\[4{z}^{2}+6z-4\]

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.)
\[2(\frac{4{z}^{2}}{2}+\frac{6z}{2}-\frac{4}{2})\]

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

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

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

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

Done
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