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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The factorized form of x³-3x²-9x-5 is (x+1)(x+1)(x-5). Factorization or factoring is a process in Mathematics that consists of writing a number or another mathematical object as a product of several factors. In simpler terms, it finds the factors of algebraic equations and represents them in simple form instead of expanded form. These are usually smaller or simpler objects of the same kind.

Table of content

1. Factorized Form of x³-3x²-9x-5
2. Polynomial
3. Four Main Polynomial Operations
4. Factorize the Equation: x^3-3x^2-9x-5

Factorized Form of x³-3x²-9x-5

The process to factorize the equation of x³-3x²-9x-5 is provided below.

Step 1: Split the middle terms in above equation:

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 the equation

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

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

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

Polynomial

Polynomial is formed composed of the phrases Nominal, which means erms, and Poly, which means many. An expression that consists of variables, constants, and exponents that are 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.

Four Main Polynomial Operations

The main four types of polynomial operations are listed and explained below in detail.

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.
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.
Polynomial Multiplication – A polynomial of a higher degree is always produced when two or more polynomials are multiplied (unless one of them is a constant polynomial).
Polynomial Division – A polynomial may or may not come from the division of two polynomials.

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