Question

Find two different polynomial functions that have a zero at 2 of multiplicity 5 and a zero at -4 of multiplicity 3?

Answer 1

Required polynomial is (x - 2)^5 (x + 4)^3 = (x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32)(x^3 + 12x^2 + 48x + 64) = x^8 + 2x^7 - 32x^6 - 16x^5 + 400x^4 - 352x^3 - 1664x^2 + 3584x - 2048