Which of the following polynomials has zeros at x=-4 and x=7?

Remark

This requires that you factor all 4 choices. There is no other way to do it. However you can eliminate one of the choices.

C might give you a factor of 1/7 but it will not give you 7. The same can be said about a and b. They do factor, but you will get a fraction in both answers. That means your answer is probably D, which we should check out first.

Solution

x ^2 - 3x - 28 = 0

(x - 7) (x + 4) = 0 These factors come about because the numbers 4 and 7 are relatively close together. Your other choices for factors would be 2 and 14 or 1 and 28. These numbers are just too far apart when subtracted to be the answer.

x - 7 = 0

x = 7

x + 4 = 0

x = - 4

D is indeed your answer.

C

No factors will work. This cannot be factored into integer results.

B

4x^2 - 49 Use the difference of squares.

(2x - 7) (2x + 7)

x = 7/2 or x = - 7/2 Not a choice

A

(x + 1) (4x - 11) = 0

x = - 1 or

x = 11/4

A is not the answer