Problem of the Week

Updated at Jan 27, 2014 4:04 PM

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

How would you find the factors of \(12{y}^{4}+100{y}^{3}+112{y}^{2}\)?

Check out the solution below!



\[12{y}^{4}+100{y}^{3}+112{y}^{2}\]

1
Find the Greatest Common Factor (GCF).
GCF = \(4{y}^{2}\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[4{y}^{2}(\frac{12{y}^{4}}{4{y}^{2}}+\frac{100{y}^{3}}{4{y}^{2}}+\frac{112{y}^{2}}{4{y}^{2}})\]

3
Simplify each term in parentheses.
\[4{y}^{2}(3{y}^{2}+25y+28)\]

4
Split the second term in \(3{y}^{2}+25y+28\) into two terms.
\[4{y}^{2}(3{y}^{2}+21y+4y+28)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[4{y}^{2}(3y(y+7)+4(y+7))\]

6
Factor out the common term \(y+7\).
\[4{y}^{2}(y+7)(3y+4)\]

Done
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