Question

Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.)

x = -8,0, 1; n = 3

Answer 1

Answer: f(x) = x³ + 7x² -8x

Explanation:

Zeros means that at that x-value, the graph crosses the x-axis and y = 0. Hence, to meet those criteria, the function would be:

`f(x)=x(x+8)(x-1)`

At those three x-values, the corresponding y-values would equal 0.

Multiply them out to find the polynomial function:

`f(x)=x(x+8)(x-1)=x(x^(2) -x+8x-8)=x^(3) +7x^(2) -8x`