Factoring Polynomials Examples
Example 1: Factorize 7x2 – 21x.
Solution:
Let f(x) = 7x2 – 21x
As 7 and x is common in each term of the given polynomial
f(x) = 7x(x -3)
Hence, 7x and x – 3 are the factors of the given polynomial.
Example 2: What are the factors of y2-8y+7?
Solution:
Let g(y) = y2-8y+7
⇒ g(y) = y2-8y+7
⇒ g(y) = y2-7y-y+7
⇒ g(y) = y(y-7)-(y-7)
⇒ g(y) = (y-7)(y-1)
Thus, y-7 and y-1 are the factors of y2-8y+7.
Example 3: Factorize x2+x-1.
Solution:
Comparing x2+x-1 with the general quadratic expression ax2+bx+c, we get
a=1, b=1 and c=-1
Using Sridharacharya Formula,
Thus, using factor theorem and are the factors of the given polynomial.
Example 4: Factorize x3-5x2+9x-5.
Solution:
Let f(x) = x3-5x2+9x-5
As constant part is 5, and it’s divisors are ±1, ±5.
f(1) = 1 – 5 +9 -5 = 0
Thus, x-1 is factor of f(x).
Now, dividing f(x) using long division by x-1
Thus, f(x) = (x-1)(x2-4x+5)
As x2-4x+5 can’t be factored further,
So, x-1 and x2-4x+5 are the required factors of x3-5x2+9x-5.
Factoring Polynomials
Factoring Polynomials: A basic algebraic concept called factoring polynomials involves breaking down a polynomial equation into simpler parts. Factoring can be used to solve equations, simplify complicated expressions, and locate the roots or zeros of polynomial functions.
In several fields of mathematics, including engineering, physics, and computer science, the ability to factor is a crucial skill. Finding the common factors, or roots, of the equation and breaking them down into a set of simpler expressions are the general steps involved in factoring a polynomial.
In this article, we have provided details about factoring polynomials, steps to factorize polynomials, with solved examples and practice problems on it.
Table of Content
- What is Factoring Polynomials?
- Steps for Factoring Polynomials – How to Factorise
- Techniques for Factoring Polynomials
- Algebraic Identities
- Long Division Method
- Factor Theorem
- Reminder Theorem
- Factoring Polynomials Examples
- Factoring Polynomials Worksheet