A cubic polynomial in one variable can be generally written as

$f(x) = ax^{3}+bx^{2}+cx+d$ where x is the variable and a, b, c and d are the constants.

Any cubic polynomial in the form $x^ {3} +y^ {3} $ is called perfect cubic polynomial.

It has a special formula

$x^ {3} +y^ {3} =(x+y) (x^ {2}-xy+y^{2}) $

$x^ {3} - y^ {3}=(x-y) (x^ {2} +xy+y^ {2}) $

Factoring is the process by which a polynomial can be written as the product of two or more simpler polynomialThe first thing is to check if there exist a greatest common factor (GCF), generally called, common factor, in the polynomial.

For example $21y^{2} – 14y^{3}$

The following steps has to be followed.

- Identify each of the terms and its factors in the polynomial

$21y^{2}=1*3*5*y*y $

$14y^{3}= 1*3*7*y*y*y$

- Find the GCF

- Write the GCF outside the parenthesis

- Divide each term by the GCD

- Write then inside the parentheses

So, $21y^{2} – 14y^{3} = 7y^{2}(3+2y)$

Let consider another example: $y(2x^{2}+1)-5(2x^{2}+1)$

This follows the same steps.

- Identify each of the terms and its factors in the polynomial

$y (2x^{2}+1)= y*(2x^{2}+1)$ and $5(2x^{2}+1)= 5*(2x^{2}+1)$

- Find the common factor

- Write the GCF outside the parenthesis

- Divide each term by the GCD

- Write then inside the parentheses

So, $y(2x+1)-5(2x+1) = (2x^{2}+1)(y-5)$

A polynomial can be called prime if it cannot be factored into product of polynomials other than 1 and the polynomial itself.

For example $x^{3} – 4w^{2}$