Question

factor.
t^2 + 7t + 12

Explanation:

Step1: Find two numbers

We need two numbers that multiply to 12 and add up to 7. The numbers are 3 and 4 since \(3\times4 = 12\) and \(3 + 4=7\).

Step2: Factor the quadratic

We rewrite the middle - term and factor by grouping. \(t^{2}+7t + 12=t^{2}+3t+4t + 12=t(t + 3)+4(t + 3)=(t + 3)(t + 4)\)

Answer:

\((t + 3)(t + 4)\)