Problem of the Week

Updated at Aug 7, 2017 12:35 PM

This week's problem comes from the algebra category.

How can we compute the factors of \(10{x}^{2}-24x+8\)?

Let's begin!



\[10{x}^{2}-24x+8\]

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.)
\[2(\frac{10{x}^{2}}{2}+\frac{-24x}{2}+\frac{8}{2})\]

3
Simplify each term in parentheses.
\[2(5{x}^{2}-12x+4)\]

4
Split the second term in \(5{x}^{2}-12x+4\) into two terms.
\[2(5{x}^{2}-2x-10x+4)\]

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

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

Done
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