# Factoring cubic Polynomials

Any polynomial with degree three is called a polynomial of degree three or generally as cubic polynomial.
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
Here there are two terms $21y^{2}$and $14y^{3}$
$21y^{2}=1*3*5*y*y$
$14y^{3}= 1*3*7*y*y*y$
• Find the GCF
Here GCF=$1*7*y*y=7y^{2}$
• Write the GCF outside the parenthesis
Here $7y^{2}( )$
• Divide each term by the GCD
Here, $\frac{21y^{2}}{7y^{2}}=3$ and $\frac{14y^{3}}{7y^{2}}=2y$
• Write then inside the parentheses
$7y^{2}(3+2y)$
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
In this problem, there are only two terms $y (2x^{2}+1)$ and $5(2x^{2}+1)$
$y (2x^{2}+1)= y*(2x^{2}+1)$ and $5(2x^{2}+1)= 5*(2x^{2}+1)$
• Find the common factor
It can be seen that the common factor here is a binomial, that is $(2x^{2}+1)$
• Write the GCF outside the parenthesis
$(2x^{2}+1)( ) • Divide each term by the GCD Here,$\frac{ y(2x^{2}+1)}{ (2x^{2}+1)}=y$and$\frac{ 5(2x^{2}+1)}{ (2x^{2}+1)}=5$• Write then inside the parentheses$(2x^{2}+1)( y+5)$So,$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}\$