Question

1. $2m^2 + 17m - 30$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-30)= -60\) and add up to \(17\). The numbers are \(20\) and \(-3\) since \(20\times(-3)= -60\) and \(20 + (-3)=17\).

Step2: Split the middle term

Rewrite the middle term \(17m\) as \(20m - 3m\) in the expression \(2m^{2}+17m - 30\):
\(2m^{2}+20m - 3m - 30\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2m^{2}+20m)+(-3m - 30)\)
Factor out the greatest common factor from each group:
\(2m(m + 10)-3(m + 10)\)

Step4: Factor out the common binomial

Factor out \((m + 10)\) from both terms:
\((2m - 3)(m + 10)\)

Answer:

\((2m - 3)(m + 10)\)