# Problem of the Week

## Updated at Apr 1, 2024 9:48 AM

This week we have another algebra problem:

How can we factor $$20{w}^{2}-38w+14$$?

Let's start!

$20{w}^{2}-38w+14$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$20{w}^{2}$$, $$-38w$$, and $$14$$?It is $$2$$.2 What is the highest degree of $$w$$ that divides evenly into $$20{w}^{2}$$, $$-38w$$, and $$14$$?It is 1, since $$w$$ 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{w}^{2}}{2}+\frac{-38w}{2}+\frac{14}{2})$3 Simplify each term in parentheses.$2(10{w}^{2}-19w+7)$4 Split the second term in $$10{w}^{2}-19w+7$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$10\times 7=70$2 Ask: Which two numbers add up to $$-19$$ and multiply to $$70$$?$$-5$$ and $$-14$$3 Split $$-19w$$ as the sum of $$-5w$$ and $$-14w$$.$10{w}^{2}-5w-14w+7$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(10{w}^{2}-5w-14w+7)$5 Factor out common terms in the first two terms, then in the last two terms.$2(5w(2w-1)-7(2w-1))$6 Factor out the common term $$2w-1$$.$2(2w-1)(5w-7)$Done2*(2*w-1)*(5*w-7)