# Problem of the Week

## Updated at Mar 11, 2024 9:46 AM

For this week we've brought you this algebra problem.

How would you find the factors of $$20{y}^{2}+2y-4$$?

Here are the steps:

$20{y}^{2}+2y-4$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$20{y}^{2}$$, $$2y$$, and $$-4$$?It is $$2$$.2 What is the highest degree of $$y$$ that divides evenly into $$20{y}^{2}$$, $$2y$$, and $$-4$$?It is 1, since $$y$$ is not in every term.3 Multiplying the results above,The GCF is $$2$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$2$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$2(\frac{20{y}^{2}}{2}+\frac{2y}{2}-\frac{4}{2})$3 Simplify each term in parentheses.$2(10{y}^{2}+y-2)$4 Split the second term in $$10{y}^{2}+y-2$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$10\times -2=-20$2 Ask: Which two numbers add up to $$1$$ and multiply to $$-20$$?$$5$$ and $$-4$$3 Split $$y$$ as the sum of $$5y$$ and $$-4y$$.$10{y}^{2}+5y-4y-2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(10{y}^{2}+5y-4y-2)$5 Factor out common terms in the first two terms, then in the last two terms.$2(5y(2y+1)-2(2y+1))$6 Factor out the common term $$2y+1$$.$2(2y+1)(5y-2)$Done2*(2*y+1)*(5*y-2)