# Problem of the Week

## Updated at Apr 23, 2018 11:41 AM

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

How can we compute the factors of $$49{x}^{2}+7x-42$$?

Here are the steps:

$49{x}^{2}+7x-42$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$49{x}^{2}$$, $$7x$$, and $$-42$$?It is $$7$$.2 What is the highest degree of $$x$$ that divides evenly into $$49{x}^{2}$$, $$7x$$, and $$-42$$?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{49{x}^{2}}{7}+\frac{7x}{7}-\frac{42}{7})$3 Simplify each term in parentheses.$7(7{x}^{2}+x-6)$4 Split the second term in $$7{x}^{2}+x-6$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$7\times -6=-42$2 Ask: Which two numbers add up to $$1$$ and multiply to $$-42$$?$$7$$ and $$-6$$3 Split $$x$$ as the sum of $$7x$$ and $$-6x$$.$7{x}^{2}+7x-6x-6$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$7(7{x}^{2}+7x-6x-6)$5 Factor out common terms in the first two terms, then in the last two terms.$7(7x(x+1)-6(x+1))$6 Factor out the common term $$x+1$$.$7(x+1)(7x-6)$Done 7*(x+1)*(7*x-6)