Question

What are the real zeros of the polynomial function f(x)=8x3−33x2+43x−18 with the factor x−1? A. x=1,x=23​,x=−2 B. x=−1,x=2,x=−23​ C. x=1,x=−2,x=23​ D. x=−1,x=−23​,x=2

Answer 1

The real zeros of the polynomial function f(x)=8x3−33x2+43x−18 with the factor x−1 are x=1 and x=23.

Step-by-step explanation:

To find the real zeros of a polynomial function, we need to solve for the values of x that make the function equal to zero. In this case, the polynomial function f(x)=8x^3−33x^2+43x−18 is given, and we are told that it has a factor of x−1.

By using synthetic division or long division, we can divide the given polynomial by x−1 to find the remaining quadratic factor. The quotient will be a quadratic polynomial, which we can then solve using the quadratic formula or factoring.

After finding the solutions to the quadratic equation, we determine that the real zeros of the polynomial function f(x)=8x^3−33x^2+43x−18 with the factor x−1 are x=1 and x=23​.