Systems of Equations
Adding and Subtracting Rational Expressions with Different Denominators
Graphing Linear Equations
Raising an Exponential Expression to a Power
Horizontal Line Test
Quadratic Equations
Mixed Numbers and Improper Fractions
Solving Quadratic Equations by Completing the Square
Solving Exponential Equations
Adding and Subtracting Polynomials
Factorizing simple expressions
Identifying Prime and Composite Numbers
Solving Linear Systems of Equations by Graphing
Complex Conjugates
Graphing Compound Inequalities
Simplified Form of a Square Root
Solving Quadratic Equations Using the Square Root Property
Multiplication Property of Radicals
Determining if a Function has an Inverse
Scientific Notation
Degree of a Polynomial
Factoring Polynomials by Grouping
Solving Linear Systems of Equations
Exponential Functions
Factoring Trinomials by Grouping
The Slope of a Line
Simplifying Complex Fractions That Contain Addition or Subtraction
Solving Absolute Value Equations
Solving Right Triangles
Solving Rational Inequalities with a Sign Graph
Domain and Range of a Function
Multiplying Polynomials
Slope of a Line
Multiplying Rational Expressions
Percent of Change
Equations Involving Fractions or Decimals
Simplifying Expressions Containing only Monomials
Solving Inequalities
Quadratic Equations with Imaginary Solutions
Reducing Fractions to Lowest Terms
Prime and Composite Numbers
Dividing with Exponents
Dividing Rational Expressions
Equivalent Fractions
Graphing Quadratic Functions
Linear Equations and Inequalities in One Variable
Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
Solving Quadratic Equations
Factoring Polynomials Completely
Using Slopes to Graph Lines
Fractions, Decimals and Percents
Solving Systems of Equations by Substitution
Quotient Rule for Radicals
Prime Polynomials
Solving Nonlinear Equations by Substitution
Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
Finding the Least Common Denominator of Rational Expressions
Multiplying Rational Expressions
Expansion of a Product of Binomials
Solving Equations
Exponential Growth
Factoring by Grouping
Solving One-Step Equations Using Models
Solving Quadratic Equations by Factoring
Adding and Subtracting Polynomials
Rationalizing the Denominator
Rounding Off
The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
Dividing Monomials
Multiplying Polynomials
Adding and Subtracting Functions
Dividing Polynomials
Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Adding and Subtracting Polynomials
The Rectangular Coordinate System
Polar Form of a Complex Number
Exponents and Order of Operations
Graphing Horizontal and Vertical Lines
Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
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Adding and Subtracting Polynomials


A variable is a quantity represented by a letter.

A polynomial is the sum of terms that contain variables raised to positive integer or zero powers and that have no variables in any denominator.

A term is one of the addends in an addition expression. For example, in the expression 2x + 4, the terms are 2x and 4.

The parts of each term that are multiplied are the factors of the term. For example, in the term 2x from the example above, the factors are 2 and x.

Like terms have the same variable factors raised to the same powers. For example, in the expression 2x2 + 3x + 7 + 3x2 + 4x + 9, the 2x2 and 3x2 are like terms, the 3x and 4x are like terms, and the 7 and 9 are like terms.


Adding Polynomials

To add two polynomials, use the commutative and associative properties of addition to rewrite the sum so that like terms are grouped, and then use the distributive property to combine like terms.


Simplify (2x + 7) + ( 4x − 9)

(2x + 7) + ( 4x − 9)

 = (2x + 7) + ( 4x + (− 9))


 = 2x + 7 + 4x + (-9)
   = 2x + 4x + 7 + (-9)
   = (2 + 4)x + (-2)
   = 6x - 2


Negating Polynomials

If there is a negative sign directly preceding the parenthesis surrounding a polynomial, the negative sign applies to each term inside the parenthesis. Use the distributive property to distribute the negation to each term inside the parenthesis. You may think of the negative preceding the parenthesis as a –1, and use the rules for multiplying signed numbers.


Simplify. − (5x + 7 ) = −1(5x + 7 )

− (5x + 7 )

 = −1(5x + 7 )


 = (−1)(5x) + (−1)(7)
   = -5x + (-7)
   = -5x + (-7)
   = -5x - 7


Subtracting Polynomials

To subtract two polynomials, change the subtraction to addition of the opposite and then add.


Simplify  ( 2x + 3 )− ( 5x − 7 )

( 2x + 3 ) − ( 5x − 7 )  = ( 2x + 3 ) + (-1)( 5x − 7 )


 = ( 2x + 3 ) + (-1)( 5x + (− 7) )
   = ( 2x + 3 ) + (-1)( 5x ) + (-1)(− 7)
   = 2x  + ( -5x ) + 3 + (7)
   = (-3x) + (10)
   = -3x + 10


Evaluating Polynomials

To find the value of a polynomial at a given value of the variable, substitute the value of the variable into the polynomial everywhere the variable appears.

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