Q:

PLEASE HELP 30 PTS!!! Select ALL the correct answers. Which expressions are equivalent to the following? 30x^2-5x-10A: (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)

Accepted Solution

A:
Answer:   D:  -5(-6x^2 + x + 2)   E:  5(2x + 1)(3x − 2) Step-by-step explanation:The first two answer choices have incorrect constants (25 and 3 vs -10). 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 signThe equivalent expressions are those of choices D and E.