Question

What is the degree 3 polynomial that has zeros -3,2 and 5 and in which the coefficient of x^2 is -8?

Answer 1

For zeroes/roots r1,r2, r3
the facors of the polynomial is
(x-r1)(x-r2)(x-r3)

roots
-3,2,5
(x-(-3))(x-2)(x-5)
(x+3)(x-2)(x-5)
the coefient of the x term is -4
so mutliply the whole thing by 2

(2)(x+3)(x-2)(x-5)

expand
f(x)=2x^3-8x^2-22x+60