Answer:
D. (2x +1)(x -6)
Explanation:
You want the expression that is equivalent to 2x² -11x -6.
Choices
There are a couple of ways to go at this. One way is to eliminate the answers that make no sense: A and C. We say these are nonsense because they have an overall factor of 2. The coefficient -11 is not a multiple of 2, so there cannot be such a factor.
If you were to examine the remaining choices (after eliminating A and C), you would find the x-term of the product to be ...
B: 2x(-2) +3(x) = -4x +3x = -x
D: 2x(-6) +1x = -12x +x = -11x . . . . . the expression we're looking for
Factors
If you were to factor this equation, you would look for factors of 2·(-6) = -12 that have a sum of -11. Of course, those are -12 and 1. This means we can rewrite the equation as ...
2x² -11x -6 = 2x² -12x +x -6
= 2x(x -6) +1(x -6) . . . . . . . factor by grouping (pairs of terms)
= (2x +1)(x -6) . . . . . . . . . . matches choice D.
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