Problem of the Week

Updated at Oct 2, 2017 9:33 AM

This week we have another algebra problem:

How can we factor \(35{x}^{2}-50x+15\)?

Let's start!



\[35{x}^{2}-50x+15\]

1
Find the Greatest Common Factor (GCF).
GCF = \(5\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[5(\frac{35{x}^{2}}{5}+\frac{-50x}{5}+\frac{15}{5})\]

3
Simplify each term in parentheses.
\[5(7{x}^{2}-10x+3)\]

4
Split the second term in \(7{x}^{2}-10x+3\) into two terms.
\[5(7{x}^{2}-3x-7x+3)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[5(x(7x-3)-(7x-3))\]

6
Factor out the common term \(7x-3\).
\[5(7x-3)(x-1)\]

Done
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