# 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).1 What is the largest number that divides evenly into $$30{y}^{2}$$, $$-33y$$, and $$9$$?It is $$3$$.2 What is the highest degree of $$y$$ that divides evenly into $$30{y}^{2}$$, $$-33y$$, and $$9$$?It is 1, since $$y$$ is not in every term.3 Multiplying the results above,The GCF is $$3$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!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.1 Multiply the coefficient of the first term by the constant term.$10\times 3=30$2 Ask: Which two numbers add up to $$-11$$ and multiply to $$30$$?$$-5$$ and $$-6$$3 Split $$-11y$$ as the sum of $$-5y$$ and $$-6y$$.$10{y}^{2}-5y-6y+3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$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 3*(2*y-1)*(5*y-3)