How to Factor Polynomials

Factoring Polynomials refers to factoring a polynomial into irreducible polynomials over a given field. It gives out the factors that together form a polynomial function. A polynomial function is of the form xn + xn -1 + xn - 2 + . . . . + k = 0, where k is a constant and n is a power.Polynomials are expressions that are formed by adding or subtracting several variables called monomials. Monomials are variables that are formed with a constant and a variable of some degree. Examples of monomials are 5x3, 6a2. Monomials having different exponents such as 5x3 and 3x4 cannot be added or subtracted but can be multiplied or divided by them. Any polynomial of the form F(a) can also be written as

 

F(a) = Q(a) x D (a) + R (a)

 

using Dividend = Quotient x Divisor + Remainder.

Example

 

Solve x2-7x+12

 

Solution:

 

Given x2-7x+12

 

a=1,b=-7,c=12

 

We have x = [(-b+-root(2)(b^(2)-4ac))/(2a)]

 

x = [(7+-root(2)((-7)^(2)-4*1*12))/(2*1)]

 

x = [(7+-root(2)(49-48))/(2)]

 

x= [(7+-1)/2]

 

x=8/2=4 or x=6/2=3

 

solutions is x=4 and x=3

 

Done