Problem of the Week

Updated at Sep 12, 2022 11:29 AM

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

How can we compute the factors of \(8{y}^{2}-34y+30\)?

Check out the solution below!



\[8{y}^{2}-34y+30\]

1
Find the Greatest Common Factor (GCF).
GCF = \(2\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[2(\frac{8{y}^{2}}{2}+\frac{-34y}{2}+\frac{30}{2})\]

3
Simplify each term in parentheses.
\[2(4{y}^{2}-17y+15)\]

4
Split the second term in \(4{y}^{2}-17y+15\) into two terms.
\[2(4{y}^{2}-5y-12y+15)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(y(4y-5)-3(4y-5))\]

6
Factor out the common term \(4y-5\).
\[2(4y-5)(y-3)\]

Done
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