Problem of the Week

Updated at Mar 20, 2023 8:50 AM

This week's problem comes from the algebra category.

How can we compute the factors of \(30{y}^{2}-33y+9\)?

Let's begin!



\[30{y}^{2}-33y+9\]

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.)
\[3(\frac{30{y}^{2}}{3}+\frac{-33y}{3}+\frac{9}{3})\]

3
Simplify each term in parentheses.
\[3(10{y}^{2}-11y+3)\]

4
Split the second term in \(10{y}^{2}-11y+3\) into two terms.
\[3(10{y}^{2}-5y-6y+3)\]

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

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

Done
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