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