Question

factor the polynomial.
15u² + u - 2
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. 15u² + u - 2 =

b. the polynomial cannot be factored.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(15\times(-2)= -30\) and add up to \(1\). The numbers are \(6\) and \(-5\) since \(6\times(-5)=-30\) and \(6 + (-5)=1\).

Step2: Rewrite the middle term

Rewrite the polynomial \(15u^{2}+u - 2\) as \(15u^{2}+6u-5u - 2\).

Step3: Group and factor

Group the first two terms and the last two terms: \((15u^{2}+6u)+(-5u - 2)\). Factor out the greatest common factor from each group: \(3u(5u + 2)-1(5u + 2)\). Then factor out the common binomial factor \((5u + 2)\): \((3u - 1)(5u + 2)\).

Answer:

A. \(15u^{2}+u - 2=(3u - 1)(5u + 2)\)