Problem of the Week

Updated at Aug 25, 2025 1:52 PM

How would you find the factors of \(36{z}^{2}-66z+30\)?

Below is the solution.



\[36{z}^{2}-66z+30\]

1
Find the Greatest Common Factor (GCF).
GCF = \(6\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[6(\frac{36{z}^{2}}{6}+\frac{-66z}{6}+\frac{30}{6})\]

3
Simplify each term in parentheses.
\[6(6{z}^{2}-11z+5)\]

4
Split the second term in \(6{z}^{2}-11z+5\) into two terms.
\[6(6{z}^{2}-5z-6z+5)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[6(z(6z-5)-(6z-5))\]

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

Done
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