Question

factor.
$5y^2 - 33y + 18$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(5\times18 = 90\) and add up to \(-33\). The numbers are \(-30\) and \(-3\) since \((-30)\times(-3)=90\) and \(-30 + (-3)=-33\).

Step2: Rewrite the middle term

Rewrite \(-33y\) as \(-30y - 3y\) in the expression \(5y^{2}-33y + 18\):
\[5y^{2}-30y-3y + 18\]

Step3: Group the terms

Group the first two terms and the last two terms:
\((5y^{2}-30y)+(-3y + 18)\)

Step4: Factor out the GCF from each group

Factor out \(5y\) from the first group and \(-3\) from the second group:
\(5y(y - 6)-3(y - 6)\)

Step5: Factor out the common binomial factor

Factor out \((y - 6)\) from both terms:
\((5y - 3)(y - 6)\)

Answer:

\((5y - 3)(y - 6)\)