Question

1. 7x² - 20x - 3

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(7\times(-3)= -21\) and add up to \(-20\). The numbers are \(-21\) and \(1\) since \(-21\times1 = -21\) and \(-21 + 1=-20\).

Step2: Rewrite the middle term

Rewrite \(-20x\) as \(-21x+x\) in the quadratic expression:
\(7x^{2}-21x + x-3\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((7x^{2}-21x)+(x - 3)\)
Factor out the greatest common factor from each group:
\(7x(x - 3)+1(x - 3)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x - 3)\):
\((7x + 1)(x - 3)\)

Answer:

\((7x + 1)(x - 3)\)