polynomials equations

Question

Write a polynomial function  of least degree that has a leading coefficient of 1 and the given zeros. Write the function in standard form. -2,3.6

Answer 1

(x+2)(x-3)(x-6) just make factors out of each root, with x minus the root

Then multiply the 3 factors to get a 3rd degree polynomial

(x+2)(x-3)=x^2-x-6. Multiply that by x-6

x^3-7x^2+36 has leading coefficient of 1 for the cubed term.

Check the answer, set the 3 termed cubic polynomial equal to zero. Then substitute each of the roots for x, and check to see if the polynomial = 0

-2 cubed -7 (-2) squared +36 = -8-28+36=0

3 cubed -7(9)+36=27-63+36=0

6 cubed -7(36)+36=218-252+36=0