Question

1. $x^2 + 3x - 70$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-70\) and add up to \(3\). Let's list the factor pairs of \(70\): \(1\) and \(70\), \(2\) and \(35\), \(5\) and \(14\), \(7\) and \(10\). Among these, \(10\) and \(-7\) work because \(10\times(-7)= -70\) and \(10 + (-7)=3\).

Step2: Factor the quadratic

Using the numbers we found, we can rewrite the middle term of the quadratic expression \(x^{2}+3x - 70\) as follows:
\(x^{2}+10x-7x - 70\)
Now, we group the first two terms and the last two terms:
\((x^{2}+10x)-(7x + 70)\)
Factor out the greatest common factor from each group:
\(x(x + 10)-7(x + 10)\)
Now, we can factor out the common binomial factor \((x + 10)\):
\((x + 10)(x - 7)\)

Answer:

\((x + 10)(x - 7)\)