Simplifying Polynomial Expressions

Simplifying Polynomial Expressions

Do you want to know how to simplify polynomial expressions? In this article, you learn how to simplify polynomial expressions easily.

Step by step guide to solve simplifying polynomial expressions

  • In mathematics, a polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, multiplication, and non–negative integer exponents of variables.
  • \(P(x)= a_{n} x^n \ + \ a_{n-1} x^{n \ – \ 1} \ + … + \ a_{2} x^2 \ + \ a_{1} x \ + \ a_{0}\)
  • To simplify a polynomial expression, find like terms (terms with same varibale (variables) and same powers. Then combine them.

Example 1:

Simplify this Polynomial Expression. \(x^2 \ – \ 5 \ x^3 \ + \ 2 \ x^4 \ – \ 4 \ x^3=\)

Solution:

Combine “like” terms: \(− \ 5 x^{3} \ − \ 4 x^{3}= − \ 9x^{3}\)
Then: \(x^2 \ − \ 5 x^{3} \ + \ 2 x^{4} \ − \ 4 x^{3}=x^{2} \ − \ 9 x^{3} \ + \ 2 x^{4}\)
Then write in standard form: \(=2x^{4} \ − \ 9x^{3} \ + \ x^{2} \)

Example 2:

Simplify this Polynomial Expression. \((2x^{2} \ – \ x^3 ) \ – \ (x^{3} \ – \ 4 x^{2} )=\)

Solution:

First use distributive property: \(→\) multiply \((−)\) into \(x^{3} \ − \ 4x^{ 2}\)
\(2 x^{2} \ − \ x^{3} \ − \ x^{3} \ + \ 4x^{2} \)
Then combine “like” terms: \(2x^{2} \ − \ x^{3} \ − \ x^{3} \ + \ 4x^{2}=6x^{2} \ − \ 2x^{3}\)
And write in standard form: \(=− \ 2x^{3} \ + \ 6x^{2}\)

Example 3:

Simplify this Polynomial Expression. \(4x^2-5x^3+15x^4-12x^3=\)

Solution:

Combine “like” terms: \(-5x^3-12x^3= -17x^3\)
Then: \(4x^2-5x^3+15x^4-12x^3=4x^2-17x^3+15x^4\)
Then write in standard form: \(4x^2-17x^3+15x^4=15x^4-17x^3+4x^2\)

Example 4:

Simplify this expression. \((2x^2-x^4 )-(4x^4-x^2 )=\)

Solution:

First use distributive property: \(→\) multiply \((-)\) into \((4x^4-x^2 ) \)

\( (2x^2-x^4 )-(4x^4-x^2 )=2x^2-x^4-4x^4+x^2 \)
Then combine “like” terms: \(2x^2-x^4-4x^4+x^2=3x^2-5x^4\)
And write in standard form: \(3x^2-5x^4=-5x^4+3x^2\)

Exercises

Simplify each polynomial.

  • \(\color{blue}{4x^5 – 5x^6 + 15x^5 – 12x^6 + 3 x^6}\)
  • \(\color{blue}{(– 3x^5 + 12 – 4x) + (8x^4 + 5x + 5x^5)}\)
  • \(\color{blue}{10x^2 – 5x^4 + 14x^3 – 20x^4 + 15x^3 – 8x^4}\)
  • \(\color{blue}{– 6x^2 + 5x^2 – 7x^3 + 12 + 22}\)
  • \(\color{blue}{12x^5 – 5x^3 + 8x^2 – 8x^5}\)
  • \(\color{blue}{5x^3 + 1 + x^2 – 2x – 10x}\)

Download Simplifying Polynomial Expressions Worksheet

Answers

  • \(\color{blue}{– 14x^6 + 19x^5}\)
  • \(\color{blue}{2x^5 + 8x^4 + x + 12}\)
  • \(\color{blue}{–33x^4 + 29x^3 + 10x^2}\)
  • \(\color{blue}{–7x^3 – x^2 + 34}\)
  • \(\color{blue}{4x^5 – 5x^3 + 8x^2}\)
  • \(\color{blue}{5x^3 + x^2 – 12x + 1}\)

Related to "Simplifying Polynomial Expressions"

MAP Grade 7 Math FREE Sample Practice Questions
MAP Grade 7 Math FREE Sample Practice Questions
The Ultimate SSAT Lower Level Math Formula Cheat Sheet
The Ultimate SSAT Lower Level Math Formula Cheat Sheet
Full-Length ISEE Lower Level Math Practice Test-Answers and Explanations
Full-Length ISEE Lower Level Math Practice Test-Answers and Explanations
Full-Length ISEE Lower Level Math Practice Test
Full-Length ISEE Lower Level Math Practice Test
10 Most Common Grade 6 MEAP Math Questions
10 Most Common Grade 6 MEAP Math Questions
Georgia Milestones Assessment System Math Grade 3 Practice Test Questions
Georgia Milestones Assessment System Math Grade 3 Practice Test Questions
FREE Grade 4 OST Math Practice Test
FREE Grade 4 OST Math Practice Test
Algebra 1 Worksheets
Algebra 1 Worksheets
The Ultimate ISEE Middle Level Math Formula Cheat Sheet
The Ultimate ISEE Middle Level Math Formula Cheat Sheet
NYSE Grade 7 Math FREE Sample Practice Questions
NYSE Grade 7 Math FREE Sample Practice Questions

Leave a Reply

Your email address will not be published. Required fields are marked *

30% OFF

Download Instantly

X

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…