Question

1. $7x^2 + 30x - 25$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(7\times(-25)= - 175\) and add up to \(30\). The numbers are \(35\) and \(- 5\) since \(35\times(-5)=-175\) and \(35+( - 5)=30\).

Step2: Split the middle term

Rewrite the middle term \(30x\) as \(35x-5x\):
\(7x^{2}+35x - 5x-25\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((7x^{2}+35x)-(5x + 25)\)
Factor out the common factors from each group:
\(7x(x + 5)-5(x + 5)\)

Step4: Factor out the common binomial

Factor out \((x + 5)\):
\((7x-5)(x + 5)\)

Answer:

\((7x - 5)(x + 5)\)