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 42t2+7t4942{t}^{2}+7t-49?

Here are the steps:



42t2+7t4942{t}^{2}+7t-49

1
Find the Greatest Common Factor (GCF).
GCF = 77

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
7(42t27+7t7497)7(\frac{42{t}^{2}}{7}+\frac{7t}{7}-\frac{49}{7})

3
Simplify each term in parentheses.
7(6t2+t7)7(6{t}^{2}+t-7)

4
Split the second term in 6t2+t76{t}^{2}+t-7 into two terms.
7(6t2+7t6t7)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))7(t(6t+7)-(6t+7))

6
Factor out the common term 6t+76t+7.
7(6t+7)(t1)7(6t+7)(t-1)

Done