Factorization of Polynomial 2x² +4x

Objective

To factorize a polynomial 2x²+4x

What is a Polynomial?

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

What is Factorization?

  • An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
  • Expressions that contain exactly one, two, and three terms are called monomials, binomials, and trinomials respectively. In general, any expression containing one or more terms with non-zero coefficients (and with variables having non-negative integers as exponents) is called a polynomial.
  • An identity is an equality, which is true for all values of the variables in the equality. On the other hand, an equation is true only for certain values of its variables. An equation is not an identity.
  • The following are the standard identities:     

       (a + b)² = a² + 2ab + b²

       (a - b)² = a² - 2ab + b²

Methods of Factorization

  • By splitting the middle term=>The method of Splitting the Middle Term by factorization is where you divide the middle term into two factors. We know that composite numbers can be expressed as the product of prime numbers. For example, 42=2×3×7. Here, 2,3 and 7 are the prime factors of 42.
  • By using factor theorem=>According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

Pre-requisite

Area of Rectangle: Let us say a rectangle ABCD of length=x breadth=1 Then area of rectangle ABCD can be defined as=x

Area of Square: Let us say a square ABCD of side=x Then area of square ABCD can be defined as=x²