# Problem of the Week

## Updated at Oct 2, 2017 9:33 AM

This week we have another algebra problem:

How can we factor $$35{x}^{2}-50x+15$$?

Let's start!

$35{x}^{2}-50x+15$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$35{x}^{2}$$, $$-50x$$, and $$15$$?It is $$5$$.2 What is the highest degree of $$x$$ that divides evenly into $$35{x}^{2}$$, $$-50x$$, and $$15$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$5$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$5$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$5(\frac{35{x}^{2}}{5}+\frac{-50x}{5}+\frac{15}{5})$3 Simplify each term in parentheses.$5(7{x}^{2}-10x+3)$4 Split the second term in $$7{x}^{2}-10x+3$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$7\times 3=21$2 Ask: Which two numbers add up to $$-10$$ and multiply to $$21$$?$$-3$$ and $$-7$$3 Split $$-10x$$ as the sum of $$-3x$$ and $$-7x$$.$7{x}^{2}-3x-7x+3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$5(7{x}^{2}-3x-7x+3)$5 Factor out common terms in the first two terms, then in the last two terms.$5(x(7x-3)-(7x-3))$6 Factor out the common term $$7x-3$$.$5(7x-3)(x-1)$Done 5*(7*x-3)*(x-1)