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).
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.
\[4(2{x}^{2}+14x+3x+21)\]

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
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