Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Fourth-degree and a single zero of 2 2 .

Answer 1

I think it right

Enjoy!

x-2)^4 = (x^2-4x +4)^2 = x^4 - 8x^3 + 24x^2 -32x + 16

plug x=2 into the 4th degree polynomial and it = 0.

x=2, take the zero and change its sign to -2, then stick an x in front of it to get x-2. Since there's only one zero, that means it has multiplicity 4, given a 4th degree polynomial. Make the 4 an exponent to get:
(x-2)^4, then multiply it out: (x-2)(x-2)(x-2)(x-2) Use FOIL to get (x^2-4x+4)(x^2-4x+4).
then with some long division you get the quartic polynomial, of degree 4, with an x^4 term.