# Problem of the Week

## Updated at Jan 3, 2022 4:21 PM

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

How can we factor $$14{x}^{2}-7x-21$$?

Here are the steps:

$14{x}^{2}-7x-21$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$14{x}^{2}$$, $$-7x$$, and $$-21$$?It is $$7$$.2 What is the highest degree of $$x$$ that divides evenly into $$14{x}^{2}$$, $$-7x$$, and $$-21$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$7$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$7$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$7(\frac{14{x}^{2}}{7}+\frac{-7x}{7}-\frac{21}{7})$3 Simplify each term in parentheses.$7(2{x}^{2}-x-3)$4 Split the second term in $$2{x}^{2}-x-3$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times -3=-6$2 Ask: Which two numbers add up to $$-1$$ and multiply to $$-6$$?$$2$$ and $$-3$$3 Split $$-x$$ as the sum of $$2x$$ and $$-3x$$.$2{x}^{2}+2x-3x-3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$7(2{x}^{2}+2x-3x-3)$5 Factor out common terms in the first two terms, then in the last two terms.$7(2x(x+1)-3(x+1))$6 Factor out the common term $$x+1$$.$7(x+1)(2x-3)$Done 7*(x+1)*(2*x-3)