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 6t2−8t+26{t}^{2}-8t+2?

Let's begin!



6t2−8t+26{t}^{2}-8t+2

1
Find the Greatest Common Factor (GCF).
GCF = 22

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2(6t22+−8t2+22)2(\frac{6{t}^{2}}{2}+\frac{-8t}{2}+\frac{2}{2})

3
Simplify each term in parentheses.
2(3t2−4t+1)2(3{t}^{2}-4t+1)

4
Split the second term in 3t2−4t+13{t}^{2}-4t+1 into two terms.
2(3t2−t−3t+1)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))2(t(3t-1)-(3t-1))

6
Factor out the common term 3t−13t-1.
2(3t−1)(t−1)2(3t-1)(t-1)

Done
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