Factors and Zeros of Polynomials

Let $p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots +a_1x+a_0$ be a polynomial. If $p(a)=0$ , then $a$ is a zero of the polynomial and a solution of the equation $p(x)=0$ . Furthermore, $(x-a)$ is a factor of the polynomial.