How to Simplify Polynomial Expressions? (+FREE Worksheet!)
Do you want to know how to simplify polynomial expressions? In this article, you learn how to simplify polynomial expressions easily.
Related Topics
- How to Translate Phrases into an Algebraic Statement
- How to Simplify Variable Expressions
- How to Use the Distributive Property
- How to Evaluate One Variable
- How to Evaluate Two Variables
Step-by-step guide to 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 the same variable (variables) and same powers. Then combine them.
The Absolute Best Books to Ace Pre-Algebra to Algebra II
Simplifying Polynomial Expressions – Example 1:
Simplify this Polynomial Expression. \(x^2 \ – \ 5 x^3 \ + \ 2x^4 \ – \ 4x^3=\)
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: \(=2x^{4} \ − \ 9x^{3} \ + \ x^{2} \)
Simplifying Polynomial Expressions – Example 2:
Simplify this Polynomial Expression. \((2x^{2} \ – \ x^3 ) \ – \ (x^{3} \ – \ 4 x^{2} )=\)
Solution:
First use distributive property: \(→\) multiply \((−)\) into \(x^{3} \ − \ 4x^{ 2}\)
\((2x^{2} \ – \ x^3 ) \ – \ (x^{3} \ – \ 4 x^{2} )=\) \(2 x^{2} \ − \ x^{3} \ − \ x^{3} \ + \ 4x^{2} \)
Combine “like” terms: \(2x^{2} + \ 4x^{2}=6x^{2} \ , − x^{3} \ − \ x^{3} \ = − \ 2x^{3}\)
Then \(2x^{2} \ − \ x^{3} \ − \ x^{3} \ + \ 4x^{2}=6x^{2} \ − \ 2x^{3}\)
And write in standard form: \(=− \ 2x^{3} \ + \ 6x^{2}\)
Simplifying Polynomial Expressions – 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: \(=\) \( 15x^4-17x^3+4x^2\)
The Best Book to Help You Ace Pre-Algebra
Simplifying Polynomial Expressions – Example 4:
Simplify this expression. \((2x^2-x^4 )-(4x^4-x^2 )=\)
Solution:
First use distributive property: \(→\) multiply \((-)\) into \((4x^4-x^2 ) \)
\( (2x^2-x^4 )-(4x^4-x^2 )=2x^2-x^4-4x^4+x^2 \)
Combine “like” terms: \(2x^2+x^2=3x^2\), \(-x^4-4x^4=-5x^4\)
Then: \(2x^2-x^4-4x^4+x^2=3x^2-5x^4\)
And write in standard form: \(=\) \(-5x^4+3x^2\)
Exercises for Simplifying Polynomial Expressions
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
- \(\color{blue}{– 14x^6 + 19x^5}\)
- \(\color{blue}{2x^5 + 8x^4 + x + 12}\)
- \(\color{blue}{–33x^4 + 29x^3 + 10x^2}\)
- \(\color{blue}{–7x^3 – x^2 + 34}\)
- \(\color{blue}{4x^5 – 5x^3 + 8x^2}\)
- \(\color{blue}{5x^3 + x^2 – 12x + 1}\)
The Greatest Books for Students to Ace the Algebra
Related to This Article
More math articles
- How to Graph Inverse Trigonometric Functions?
- Back to School Essentials: Why “Pre-Algebra for Beginners” Should Be on Your List
- How to Find Units of Time Comparison
- Top 10 Tips to ACE the GED Math Test
- What Is a Monomial?
- How to Solve Double Angle Identities?
- Ratio, Proportion and Percentages Puzzle -Critical Thinking 10
- How to Find a Coordinate: Dilation
- Equipment Needed for Online Math Teaching
- Unlocking the Secrets of Similar Polygons: Shape, Size, and Proportions!
What people say about "How to Simplify Polynomial Expressions? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.