Factorize the Equation: x^3-3x^2-9x-5

By K Balaji|Updated : November 12th, 2022

The factorized form of x3-3x2-9x-5 is (x+1)(x+1)(x-5).

Step 1: Split the middle terms in above eqaution

Let f(x)=x3-3x2-9x-5

f(x)=x3+x2-4x2-4x-5x-5

Taking common in above equation

f(x)=x2(x+1)-4x(x+1)-5(x+1)

f(x)=(x+1)(x2-4x-5)

Step 2: Factorize the quadratic equation

f(x)=(x+1)(x2-5x+x-5)

Taking common from equation

f(x)=(x+1)x(x-5)+1(x-5)

f(x)=(x+1)(x-5)(x+1)

Hence, the factorized form of the polynomial x3-3x2-9x-5 is (x+1)(x+1)(x-5).

Polynomial

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

There are four main polynomial operations which are:

  1. Polynomial addition - When combining polynomials, always combine like terms, that is, terms with the same variable and power. A polynomial of the same degree is produced whenever polynomials are added.
  2. Polynomial Subtraction - The sole distinction between subtracting polynomials and adding them is the type of operation. Therefore, to find the answer, subtract the like phrases. It is important to remember that subtracting polynomials yields a polynomial of the same degree.
  3. Polynomial Multiplication: A polynomial of higher degree is always produced when two or more polynomials are multiplied (unless one of them is a constant polynomial).
  4. Polynomial division - A polynomial may or may not come from the division of two polynomials.

Summary:-

Factorize the Equation: x^3-3x^2-9x-5

The factorized form of x3-3x2-9x-5 is (x+1)(x+1)(x-5). In Mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

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