# Problem of the Week

## Updated at Sep 16, 2013 3:19 PM

To get more practice in algebra, we brought you this problem of the week:

How would you find the factors of $$8{x}^{2}+68x+84$$?

Check out the solution below!

$8{x}^{2}+68x+84$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$8{x}^{2}$$, $$68x$$, and $$84$$?It is $$4$$.2 What is the highest degree of $$x$$ that divides evenly into $$8{x}^{2}$$, $$68x$$, and $$84$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$4$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$4$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$4(\frac{8{x}^{2}}{4}+\frac{68x}{4}+\frac{84}{4})$3 Simplify each term in parentheses.$4(2{x}^{2}+17x+21)$4 Split the second term in $$2{x}^{2}+17x+21$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times 21=42$2 Ask: Which two numbers add up to $$17$$ and multiply to $$42$$?$$14$$ and $$3$$3 Split $$17x$$ as the sum of $$14x$$ and $$3x$$.$2{x}^{2}+14x+3x+21$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4(2{x}^{2}+14x+3x+21)$5 Factor out common terms in the first two terms, then in the last two terms.$4(2x(x+7)+3(x+7))$6 Factor out the common term $$x+7$$.$4(x+7)(2x+3)$Done 4*(x+7)*(2*x+3)