1. ## polynomial

Suppose you know that 3 is one of the zeros of the polynomial p=x^3-x^2-11x+15.

Find all the other zeros.

Briefly explain why you know that you have found all of the zeros.

2. Originally Posted by gumi
Suppose you know that 3 is one of the zeros of the polynomial p=x^3-x^2-11x+15.

Find all the other zeros.

Briefly explain why you know that you have found all of the zeros.
There are 3 zeros for this polynomial....we know this because it is of degree three...and since x=3 is a zero we know that x-3 is a factor...so your p can be factored into something like $\displaystyle p=(x-3)(ax^2+bx+c)$...to obtain the quadratic synthetically divide

3. Hello, gumi!

Suppose you know that 3 is one of the zeros of: $\displaystyle p(x) \:=\:x^3-x^2-11x+15$

Find all the other zeros.
Briefly explain why you know that you have found all of the zeros.

If $\displaystyle x = 3$ is a zero of $\displaystyle p(x)$, then $\displaystyle (x-3)$ is a factor of $\displaystyle p(x).$

We find that: .$\displaystyle p(x) \;=\;(x-3)(x^2+2x-5)$

. . And the other two zeros of $\displaystyle p(x)$ are: .$\displaystyle \boxed{x \:=\:-1 \pm\sqrt{6}}$

A cubic polynomial can have at most three zeros.