Problem of the Week

Updated at Sep 11, 2023 11:59 AM

To get more practice in algebra, we brought you this problem of the week:

How can we compute the factors of \(28{x}^{2}-63x+35\)?

Check out the solution below!



\[28{x}^{2}-63x+35\]

1
Find the Greatest Common Factor (GCF).
GCF = \(7\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[7(\frac{28{x}^{2}}{7}+\frac{-63x}{7}+\frac{35}{7})\]

3
Simplify each term in parentheses.
\[7(4{x}^{2}-9x+5)\]

4
Split the second term in \(4{x}^{2}-9x+5\) into two terms.
\[7(4{x}^{2}-4x-5x+5)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[7(4x(x-1)-5(x-1))\]

6
Factor out the common term \(x-1\).
\[7(x-1)(4x-5)\]

Done
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