Problem of the Week

Updated at Nov 11, 2024 12:01 PM

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

How would you find the factors of \(42{t}^{2}+7t-49\)?

Here are the steps:



\[42{t}^{2}+7t-49\]

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.)
\[7(\frac{42{t}^{2}}{7}+\frac{7t}{7}-\frac{49}{7})\]

3
Simplify each term in parentheses.
\[7(6{t}^{2}+t-7)\]

4
Split the second term in \(6{t}^{2}+t-7\) into two terms.
\[7(6{t}^{2}+7t-6t-7)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[7(t(6t+7)-(6t+7))\]

6
Factor out the common term \(6t+7\).
\[7(6t+7)(t-1)\]

Done
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