Use the rational zeros theorem to find all the real zeros of the polynomial function. You must show the synthetic division used to factor.

Question

𝑓(𝑥) = 𝑥^3 − 4𝑥^2 − 19𝑥 − 14

a) Use the rational zeros theorem to find all the real zeros of the polynomial function. You must show the synthetic division used to factor.

b) Use the real zeros to factor 𝑓.

Show all work.

Answer 1

-1 | 1 -4 -19 -14

-1 5 14

-2 | 1 -5 -14 0

-2 14

7 | 1 -7 0

7

1 0

The remainders of 0 show that each of these is a factor by synthetic division.

The zeros are: -1,-2, 7

The factors would be f(x) = (x+1)(x+2)(x-7)