Division Alogorithm For Polynomials

A cubic polynomial can have up to zeroes.

However, if you are given only one zero, can you determine the other two?

YesNo, using polynomial division!

Consider the cubic polynomial: p(x) = x3 + 3x2 - x - 3

We are given that one zero of this polynomial is x = 1.

Step 1: Dividing by x - 1

Since x = 1 is a zero, it means p(x) is divisible by x - 1 .

Perform polynomial division of x3 + 3x2 - x - 3 by x - 1. The quotient obtained is: x2 - 2x - 3

Step 2: Factoring the Quadratic Polynomial

Now, we factorize x2 - 2x - 3: x2 - 2x - 3 = (x + 1)(x - 3)

Thus, the full factorization of the original polynomial is: (x - 1)(x + 1)(x - 3)

Step 3: Identifying All Zeroes

From the factorization (x - 1)(x + 1)(x - 3) = 0, we get the three zeroes: x = , ,