Question

which statement about $6x^2 + 7x - 10$ is true?
one of the factors is $(x + 2)$.
one of the factors is $(3x - 2)$.
one of the factors is $(2x + 5)$.
one of the factors is $(x - 5)$.

Explanation:

Step1: Factor the quadratic expression

We need to factor $6x^2 + 7x - 10$. Find two numbers that multiply to $6\times(-10)=-60$ and add to $7$. These numbers are $12$ and $-5$.
Rewrite the middle term:
$6x^2 + 12x - 5x - 10$
Group and factor:
$6x(x + 2) - 5(x + 2) = (6x - 5)(x + 2)$

Step2: Match with given options

Compare the factored form $(6x - 5)(x + 2)$ to the provided choices.

Answer:

One of the factors is $(x + 2)$.