Question

factor.
$5z^2 - 27z - 18$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times(-18)= -90\) and add up to \(-27\). The numbers are \(-30\) and \(3\) since \(-30\times3 = -90\) and \(-30 + 3=-27\).

Step2: Rewrite the middle term

Rewrite \(-27z\) as \(-30z+3z\) in the expression \(5z^{2}-27z - 18\):
\[5z^{2}-30z + 3z-18\]

Step3: Group and factor

Group the first two terms and the last two terms:
\((5z^{2}-30z)+(3z - 18)\)
Factor out the greatest common factor from each group:
\(5z(z - 6)+3(z - 6)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((z - 6)\):
\((5z + 3)(z - 6)\)

Answer:

\((5z + 3)(z - 6)\)