Question

1. ( m^2 + m - 90 )

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -90 and add up to 1. Let's list the factor pairs of 90: (1, 90), (2, 45), (3, 30), (5, 18), (6, 15), (9, 10). We need one positive and one negative number since their product is -90. The pair (10, -9) works because \(10\times(-9)= -90\) and \(10 + (-9)=1\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(m^{2}+m - 90\) as \((m + 10)(m - 9)\).

Answer:

\((m + 10)(m - 9)\)