Factoring Quadratic Polynomials

Introduction:

In algebra, the sum of a countable number of monomials is referred as  a polynomial. The way of writing a polynomial as a product of two or more simpler polynomials is referred as factorization.
The process of factorization is also known as the resolution of factors. Factoring quadratic polynomials is one of the basic operations of polynomials. The process of factoring the quadratic expression ax^2 + bx +c is explained below: Looking out for more help on Factor a Polynomial in algebra by visiting listed websites.

Method of factoring quadratic polynomials:


Let us consider the coefficients a, b and c as integers and a is not equal to 0. When the coefficients a, b and c satisfy certain conditions, the quadratic expression ax^2 + bx +c can be factorized.

First, we consider a simpler case with a = 1 and b and c as integers.Now, we have to factorize  x^2 + bx + c. We try to write the integer constant term c as a product of two integers p and q such that p + q = b. If we find solution in our attempt, then

x^2 + bx + c  =  x^2 + (p + q)x + pq

=  (x^2 + px) + (qx + pq)

=  x(x + p) + q(x + p)

=  (x + p) (x + q)

General Rule for factoring quadratic polynomials : If the constant term c of quadratic expression x^2 + bx + c can be expressed as a product of two integers p and q such that the sum p + q is the coefficient b of x, then x^2 + bx + c = (x + p)(x + q).

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Example for factoring quadratic polynomials


An example for factoring quadratic polynomials is given below:

1) Factorize x^2 + 5x + 6.

Step 1 : Possible factorization of 6 is    6 = 1 x 6

6 = 2 x 3

Step 2 : Sum of factors are                      1 + 6 = 7

2 + 3 = 5

Step 3 : Factorization:

Now we need to compare the coefficient of x and the sum of the factors. We find that the sum of the factors 2 and 3 is the coefficient of x. The factorization of quadratic expression is explained below:

x^2 + 5x + 6   =   x^2 + (2 + 3)x + 6

=   (x^2 + 2x) + (3x + 6)

=  x(x + 2) + 3(x + 2)

x^2 + 5x + 6  =  (x + 2) (x + 3)

Explain Polynomials

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Let us learn about arithmetic sequence and polynomial problems
Polynomial is an equation that is formed by adding or subtracting several variables called monomial. Monomial is a variable that is formed with a number and a letter variable to its powers. The example of monomial is 3X³. You can’t add or subtract monomials if they have different exponents such as 3X³ and 4X⁴. But you can multiply or divide them. To multiply monomials, just add the exponents of the variables and multiply the coefficients. 3X³ x 4X⁴ = 12X⁷.

Here are some additional ways to manipulate the monomials:

* (a^m)ⁿ = a^mn
* (ab)^m= a^mb^m
I hope the above explanation was useful, now let me give you some examples on polynomials.

Introduction on polynomials

Let us learn what is meant by polynomials,

let's say what a polynomial is: in words, it is a function that is built by simply adding together some power functions. For example,

More generally, a polynomial can be written as

The highest power that occurs in the polynomial, in this case n, is called the degree of the polynomial. Degree 2 polynomials are usually called quadratic polynomials and should be quite familiar; for instance, their graphs are parabolas. The numbers ai in front of the powers are called coefficients.

Hope the above explanation helped you.