Problem of the Week

Updated at Jun 18, 2018 8:31 AM

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Jun 18, 2018

For this week we've brought you this algebra problem.

How would you find the factors of \(15{x}^{2}-20x+5\)?

Here're the steps:

\[15{x}^{2}-20x+5\]

Find the Greatest Common Factor (GCF)

How?

\[GCF=5\]

Factor out the GCF (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

\[5(\frac{15{x}^{2}}{5}+\frac{-20x}{5}+\frac{5}{5})\]

Simplify each term in parentheses

\[5(3{x}^{2}-4x+1)\]

Split the second term in \(3{x}^{2}-4x+1\) into two terms

How?

\[5(3{x}^{2}-x-3x+1)\]

Factor out common terms in the first two terms, then in the last two terms

\[5(x(3x-1)-(3x-1))\]

Factor out the common term \(3x-1\)

\[5(3x-1)(x-1)\]

Done