Question

What are the factors of 2x2 + 3x – 54? Check all that apply. 2x – 9 2x – 6 2x + 6 x + 9 x – 6 x + 6

Answer 1

2x-9 and x+6
This is just a matter of factoring 2x^2 + 3x - 54. Since it's an quadratic equation, you know it has only 2 factors. There's a few hints in the equation that will help reduce the number of factors to try. First, the coefficient of 2 in the x^2 terms tells you that one of the factors will start with x and the other will start with 2x. Also the -54 term tells you that one of the factors will have a positive constant term and the other will have a negative constant term. Also the value 54 tells you that the constant terms will have absolute values of (1,54), (2, 27), (3, 18) or (6, 9), Looking at the possible factors given of
(2x – 9)
(2x – 6)
(2x + 6)
(x + 9)
(x – 6)
(x + 6)
3 of them start with 2x and 3 start with x. So the answer will be one of the 1st 3 possible factors and one of the last 3 possible factors. Let's try them out.
2x-9 : This leaves as the only possible 2nd choice of x+6. Multiplying 2x-9 with x+6 gives us 2x^2 + 3x - 54 which is the equation given, so it's the correct answer. But let's check to make sure.
Trying 2x-6 which has as its only possible partner x+9.
Multiplying 2x-6 by x+9 gives us 2x^2 + 12x - 54 which doesn't match. So it's not correct.
Trying 2x + 6 which has as its only possible partner x - 9.
Multiplying 2x + 6 by x - 9 gives us 2x^2 -12x - 54 which also doesn't match.
So the only possible answer is (2x - 9) and (x + 6).