Essentially we need to factor 2x^2 -3x -m and they tell us one of the factors is (x - 3)
When we're factoring picture doing FOIL in reverse. So if one of the first terms is x then the other would need to be 2x so that their product is 2x^2. So at this point we have it factored as
(x - 3) (2x___)
We also know the outer and inner term would need to have a sum of -3x. And with what we have factored the inner terms would have a product of - 6x (-3*2x). So the outer terms have to have a product of 3x. For the outer terms to have a product of 3x, the missing number would have to be 3, so it would factor to
(x - 3)(2x + 3)
Now multiply these to get
2x^2 -3x - 9
So we know m = 9 and D is correct.
While you could also plug in values for x, in this case you would likely need to try a few different numbers to narrow the answer choices down to one, so algebra is more efficient on this one.
Take care,
Sionainn
BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.
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