Question

factor.
$7z^2 - 20z - 3$

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: Split the middle term

Rewrite the middle term \(-20z\) using \(-21z\) and \(z\):
\(7z^{2}-21z + z-3\)

Step3: Group and factor

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

Step4: Factor out the common binomial

Factor out \((z - 3)\):
\((7z + 1)(z - 3)\)

Answer:

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