Problem of the Week

Updated at Jan 15, 2024 3:07 PM

How would you find the factors of \(30{x}^{2}-57x+21\)?

Below is the solution.



\[30{x}^{2}-57x+21\]

1
Find the Greatest Common Factor (GCF).
GCF = \(3\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[3(\frac{30{x}^{2}}{3}+\frac{-57x}{3}+\frac{21}{3})\]

3
Simplify each term in parentheses.
\[3(10{x}^{2}-19x+7)\]

4
Split the second term in \(10{x}^{2}-19x+7\) into two terms.
\[3(10{x}^{2}-5x-14x+7)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[3(5x(2x-1)-7(2x-1))\]

6
Factor out the common term \(2x-1\).
\[3(2x-1)(5x-7)\]

Done
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