Problem of the Week

Updated at Jun 25, 2018 11:17 AM

How can we compute the factors of \(10{x}^{2}-35x+25\)?

Below is the solution.



\[10{x}^{2}-35x+25\]

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.)
\[5(\frac{10{x}^{2}}{5}+\frac{-35x}{5}+\frac{25}{5})\]

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

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

5
Factor out common terms in the first two terms, then in the last two terms.
\[5(2x(x-1)-5(x-1))\]

6
Factor out the common term \(x-1\).
\[5(x-1)(2x-5)\]

Done
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