Question

factor.
15y² + 31y + 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(15\times2 = 30\) and add up to \(31\). The numbers are \(30\) and \(1\).

Step2: Split the middle term

Rewrite the middle term using these two numbers: \(15y^{2}+30y + y+2\).

Step3: Group and factor

Group the first two and last two terms: \((15y^{2}+30y)+(y + 2)\). Factor out the common factors from each group: \(15y(y + 2)+1(y + 2)\).

Step4: Factor out the common binomial

Factor out \((y + 2)\) to get \((15y + 1)(y + 2)\).

Answer:

\((15y + 1)(y + 2)\)