Beginning Algebra With Applications, Chapter 8, 8.1, Section 8.1, Problem 2

Explain why the statement is true.

a. The terms of the binomial $3x-6$ have common factor.

The common factor of $3x-6$ is $3$. So $3x-6 = 3(x - 2)$.

b. The expression $3x^2 + 15$ is not in factored form.

The factored form is $3x^2 + 15 = 3(x^2 + 5)$ and the common factor is $3$.

c. $5y - 7$ is a factor of $y(5y - 7)$.

The expanded form of the expression $y(5y-7)$ is $5y^2 - 7y$. That's why $5y-7$ is the factor.