Question

PLEASE HELP 30 PTS!!! Select ALL the correct answers. Which expressions are equivalent to the following?

30x^2-5x-10

A: (10x − 5)(3x − 5)
B: 3x(2x − 1) + 2(2x − 1)
C: 5x(6x − x − 2)
D: -5(-6x2 + x + 2)
E: 5(2x + 1)(3x − 2)
F: 5(2x − 1)(3x + 2)

Answer 1

D: -5(-6x^2 + x + 2)

E: 5(2x + 1)(3x − 2)

Explanation:

You want to identify the expressions equivalent to 30x² -5x -10.

Comparison

The first two answer choices have incorrect constants (25 and -2 vs. -10).

Factored forms

A factor of 5 is removed from the remaining answer choices, so let's remove a factor of 5 and see what we get:

30x^2 -5x -10 = 5(6x^2 -x -2)

An additional x cannot be factored from the expression, so choice C can be eliminated.

Multiplying each of these factors by -1 will make the product correspond to answer choice D.

Factoring will make it correspond to answer choice E, best verified by finding the x-term of the product of the binomial factors:

E: 2x(-2) +1(3x) = -x, as required

F: 2x(2) -1(3x) = x, wrong sign

The equivalent expressions are those of choices D and E.