Question

Write a polynomial function in standard form with zeros at 5, –4, and 1.

Answer 1

x = 5, x = -4 or x = 1


x-5=0, x+4=0 or x-1=0


(x-5)(x+4)(x-1)=0


(x-5)(x^2-x+4x-4)=0


(x-5)(x^2+3x-4)=0


x(x^2+3x-4)-5(x^2+3x-4)=0


x^3+3x^2-4x-5x^2-15x+20=0


x^3-2x^2-19x+20=0


So the polynomial in standard form that has zeros 5, -4, and 1 is x^3-2x^2-19x+20