Problem of the Week

Updated at Oct 14, 2024 1:50 PM

This week's problem comes from the algebra category.

How can we compute the factors of \(6{t}^{2}-8t+2\)?

Let's begin!



\[6{t}^{2}-8t+2\]

1
Find the Greatest Common Factor (GCF).
GCF = \(2\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[2(\frac{6{t}^{2}}{2}+\frac{-8t}{2}+\frac{2}{2})\]

3
Simplify each term in parentheses.
\[2(3{t}^{2}-4t+1)\]

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

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(t(3t-1)-(3t-1))\]

6
Factor out the common term \(3t-1\).
\[2(3t-1)(t-1)\]

Done
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