Definitions and notations

Definitions:

• Factors: Let $p(x)$, q(x) and r(x) be three polynomials such that, $p(x)\times q(x)= r(x),$ then $p(x)$ and $q(x)$ are said to be the factors of $r(x)$.

• Remainder Theorem: When a polynomial of degree $n\ge 1$ is divided by $(x-a)$, then the remainder $R$ is found by $R = p(a)$.

• Zero of a polynomial: Let $p(x) = a_0 + a_1x + a_2x^2 + \dots + a_nx^n$ be a polynomial with real coefficients. By putting $x = a$ in the polynomial $p(x)$, if $p(a)$ equals zero then, i.e. $p(a) = 0$, then $“a”$ is said to be a zero of the polynomial $p(x)$.

• Synthetic Division: Synthetic Division is a method of dividing a polynomial with a linear factor.

• Cubic Polynomial: A polynomial of order three (3) is called a cubic polynomial.