Question

If f(x)=x³-4x²-11x 30f(x)=x 3 −4x 2 −11x 30 and x-2x−2 is a factor of f(x)f(x),, what are all the zeros of f(x)?

A) x=2,x=−3,x=5
B) x=2,x=3,x=−5
C) x=−2,x=3,x=5
D) x=−2,x=−3,x=−5

Answer 1

To find the zeros of f(x)=x³-4x²-11x+30 given x-2 as a factor, we use polynomial division to obtain a quadratic equation, then solve it to find the remaining zeros, which are x=2, x=3, and x=-5.

The student has provided the function f(x)=x³-4x²-11x+30 and stated that x-2 is a factor. To find all the zeros of f(x), we can perform polynomial division, dividing the function by the factor to find the other factors. Since x=2 is a zero (due to the factor x-2), we can use synthetic division or long division to divide the polynomial and find the quotient.

The quotient will be a quadratic equation, which we can solve by factoring or using the quadratic formula. After solving the quadratic equation, we get two more zeros. If we accurately factor the polynomial and solve the quadratic equation, the final zeros would be x=2, x=3, and x=-5.