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 20z2+6z−220{z}^{2}+6z-2?

Let's begin!



20z2+6z−220{z}^{2}+6z-2

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(20z22+6z2−22)2(\frac{20{z}^{2}}{2}+\frac{6z}{2}-\frac{2}{2})

3
Simplify each term in parentheses.
2(10z2+3z−1)2(10{z}^{2}+3z-1)

4
Split the second term in 10z2+3z−110{z}^{2}+3z-1 into two terms.
2(10z2+5z−2z−1)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))2(5z(2z+1)-(2z+1))

6
Factor out the common term 2z+12z+1.
2(2z+1)(5z−1)2(2z+1)(5z-1)

Done
Cymath foriOSAndroid