Question

select the correct answer.
write the expression ( 5x(x + 9) - 7(x + 9) ) in completely factored form.

a. ( (x + 9)(x + 9) )

b. ( (5x - 7)(x + 9) )

c. ( (5x - 7)(x + 9)(x + 9) )

d. ( (5x^2 + 45x)(-7x - 63) )

Explanation:

Step1: Identify common factor

The expression $5x(x + 9) - 7(x + 9)$ has a common binomial factor of $(x+9)$.

Step2: Factor out common term

Apply the distributive property in reverse: factor $(x+9)$ out of both terms, leaving $5x - 7$ as the other factor.
Expression: $5x(x + 9) - 7(x + 9) = (5x - 7)(x + 9)$

Answer:

B. $(5x - 7)(x + 9)$