Question

Write the factored form of the equation of a polynomial that has a root of x=3, a zero of x=-2, and an x-intercept of x=-1. Then write that equation in standard form

Answer 1

`f(x)=x^3-7x-6`

Explanation:

If x = 3 is a root of a polynomial f(x), then x - 3 is a factor of this polynomial.

If x = -2 is a zero of a polynomial function f(x), then f(-2) = 0 and x - (-2) = x + 2 is a factor of f(x).

If x = -1 is an x-intercept of the function, then y = 0 and x - (-1) = x + 1 is also a factor of the function f(x).

Therefore, the polynomial expression is

`f(x)=(x-3)(x+2)(x+1)`

In standard form:

`f(x)=(x-3)(x^2+2x+x+2)=(x-3)(x^2+3x+2)=x^3+3x^2+2x-3x^2-9x-6=x^3-7x-6`