Problem of the Week

Updated at Jun 29, 2020 2:29 PM

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

How can we compute the factors of \(30{x}^{2}-44x+16\)?

Check out the solution below!



\[30{x}^{2}-44x+16\]

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.)
\[2(\frac{30{x}^{2}}{2}+\frac{-44x}{2}+\frac{16}{2})\]

3
Simplify each term in parentheses.
\[2(15{x}^{2}-22x+8)\]

4
Split the second term in \(15{x}^{2}-22x+8\) into two terms.
\[2(15{x}^{2}-10x-12x+8)\]

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

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

Done
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