How to Simplify Polynomial Expressions? (+FREE Worksheet!)

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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.

Simplifying Polynomial Expressions For education statistics and research

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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})

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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)

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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

Simplifying Polynomial Expressions

Simplify each polynomial.

• (color{blue}{4x^5 – 5x^6 + 15x^5 – 12x^6 + 3 x^6})
• (color{blue}{(, 3x^5 + 12 to 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})

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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})

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