Question

Factor completely, then place the answer in the proper location on the grid. 6a² - 8a - 30

A) 2a−5
B) (2a−5)(3a+6)
C) 3a+6
D) 6a² - 8a - 30

Answer 1

The factor completely, then place the answer in the proper location on the grid. 6a² - 8a - 30 is B) (2a−5)(3a+6)

Step-by-step explanation:

To factor the expression completely, we need to find two binomials whose product equals the original expression.

We can start by looking for the greatest common factor of the terms, which in this case is 2a. Dividing each term by 2a, we get:

2a(3a - 4) - 15

Now, we want to factor the quadratic trinomial inside the parentheses.

Since the coefficient of the quadratic term is 3, we need to find two numbers whose product is 3a and whose sum is -4.

The numbers -3a and -1 satisfy these conditions, so we can write:

2a(3a - 3)(a - 5)

Thus, the correct factorization is (2a - 3)(3a - 5). Comparing this with the options given, we can see that the correct answer is B) (2a - 3)(3a - 5).