Problem of the Week

Updated at May 24, 2021 12:47 PM

How can we compute the factors of 4z2+6z−44{z}^{2}+6z-4?

Below is the solution.



4z2+6z−44{z}^{2}+6z-4

1
Find the Greatest Common Factor (GCF).
GCF = 22

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2(4z22+6z2−42)2(\frac{4{z}^{2}}{2}+\frac{6z}{2}-\frac{4}{2})

3
Simplify each term in parentheses.
2(2z2+3z−2)2(2{z}^{2}+3z-2)

4
Split the second term in 2z2+3z−22{z}^{2}+3z-2 into two terms.
2(2z2+4z−z−2)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))2(2z(z+2)-(z+2))

6
Factor out the common term z+2z+2.
2(z+2)(2z−1)2(z+2)(2z-1)

Done
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