Question

factor.
$3y^2 - 14y - 24$

Explanation:

Step1: Identify \(a\), \(b\), \(c\)

For \(3y^2 - 14y - 24\), \(a = 3\), \(b=-14\), \(c = -24\).

Step2: Find two numbers

Find two numbers that multiply to \(a\times c=3\times(-24)= -72\) and add to \(b = -14\). The numbers are \(-18\) and \(4\) (since \(-18\times4=-72\) and \(-18 + 4=-14\)).

Step3: Split the middle term

Rewrite the middle term: \(3y^2-18y + 4y-24\).

Step4: Group and factor

Group the terms: \((3y^2 - 18y)+(4y - 24)\). Factor out common factors: \(3y(y - 6)+4(y - 6)\). Then factor out \((y - 6)\): \((3y + 4)(y - 6)\).

Answer:

\((3y + 4)(y - 6)\)