Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of 4−i, 4+i, and 5, and a leading coefficient of −5.

Question

Can someone help me with this im really stuck!

Answer 1

(x-4+i)(x-4-i)(x-5)(-5)

expand and it's a 3 degree with leading coefficent -5

=(x^2-8x+16+1)(x-5)(5)

= -5x^3 + 65x^2 -285x + 425

just change the sign of each zero, add an x, then multiply them all together, along with -5 to get the leading coefficient = -5