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 10x224x+810{x}^{2}-24x+8?

Let's begin!



10x224x+810{x}^{2}-24x+8

1
Find the Greatest Common Factor (GCF).
GCF = 22

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2(10x22+24x2+82)2(\frac{10{x}^{2}}{2}+\frac{-24x}{2}+\frac{8}{2})

3
Simplify each term in parentheses.
2(5x212x+4)2(5{x}^{2}-12x+4)

4
Split the second term in 5x212x+45{x}^{2}-12x+4 into two terms.
2(5x22x10x+4)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(5x2)2(5x2))2(x(5x-2)-2(5x-2))

6
Factor out the common term 5x25x-2.
2(5x2)(x2)2(5x-2)(x-2)

Done