Question

Write a polynomial function with zeros at x = -2, 1, and 4.

Answer 1

• a=-2
• b=1
• c=4

$\\ \sf\longmapsto f(x)=(x-a)(x-b)(x-c)$

$\\ \sf\longmapsto f(x)=(x+2)(x-1)(x-4)$

$\\ \sf\longmapsto f(x)=(x^2+x-2)(x-4)$

$\\ \sf\longmapsto f(x)=x(x^2+x-2)-4(x^2+x-2)$

$\\ \sf\longmapsto f(x)=x^3+x^2-2x-4x^2-4x+8$

$\\ \sf\longmapsto f(x)=x^3-3x^2-6x+8$