Factorization Of Polynomial

Objective

To factorize a Polynomial, say (x2+ 4x + 3)

What is a Polynomial?

A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non-negative integral power.


Concept of Linear, Quadratic and Cubic polynomial.

  • A polynomial of one term is called a monomial.   
  • A polynomial of two terms is called a binomial.
  • A polynomial of three terms is called a trinomial.
  • A polynomial of degree one is called a linear polynomial.
  • A polynomial of degree two is called a quadratic polynomial.
  • A polynomial of degree three is called a cubic polynomial.

A polynomial may contain any number of terms, one or more than one. 

  • Examples of monomials: 4x 2 , 3xy, –7z, 5xy2 , 10y, –9, 82mnp, etc.
  • Examples of binomials: a + b, 4l + 5m, a + 4, 5 –3xy, z 2 – 4y 2 , etc. 
  • Examples of trinomials: a + b + c, 2x + 3y – 5, x 2y – xy2 + y 2 , etc. 
  • Examples of polynomials: a + b + c + d, 3xy, 7xyz – 10, 2x + 3y + 7z, etc.

What is Factorization?

Factoring a polynomial is expressing the polynomial as a product of two or more factors.. 

Prerequisite for the lab:

  • Concept of Area of Rectangle:
    • Consider rectangle ABCD of  length = a and  breadth = b
    • Area of rectangle ABCD  = a*b
  • Concept of Area of Square:
    • Consider a square ABCD of side = a
    • Area of square ABCD = a * a