Question

Find a polynomial function of degree 3 with real coefficients that has the given zeros. -1, 2, -8 The Polynomial function is f(x)=x^3+___x^2-10x-16

Answer 1

The zeros are -8, -1, 2, so you can write the function as f(x)=(x-(-8))(x-(-1))(x-2)=(x+8)(x+1)(x-2).

Expand:
$(x+8)(x+1)(x-2)= \\ (x^2+x+8x+8)(x-2)= \\ (x^2+9x+8)(x-2)= \\ x^3-2x^2+9x^2-18x+8x-16= \\ x^3+7x^2-10x-16$

The function is f(x)=x³+7x²-10x-16.
The missing value is 7.