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	Scientific Notation
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	Graphing Quadratic Functions
	Polynomials
	Linear Equations and Inequalities in One Variable
	Notes on the Difference of 2 Squares
	Solving Absolute Value Inequalities
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	Solving Systems of Equations by Substitution
	Quotient Rule for Radicals
	Prime Polynomials
	Solving Nonlinear Equations by Substitution
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	Finding the Least Common Denominator of Rational Expressions
	Conjugates
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	Expansion of a Product of Binomials
	Solving Equations
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	Factoring by Grouping
	Solving One-Step Equations Using Models
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	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
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	Multiplying and Dividing Fractions 3
	Formulas
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	Adding and Subtracting Functions
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	Absolute Value and Distance
	Multiplication and Division with Mixed Numbers
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	The Rectangular Coordinate System
	Polar Form of a Complex Number
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	Invariants Under Rotation
	The Addition Method
	Solving Linear Inequalities in One Variable
	The Pythagorean Theorem

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Adding and Subtracting Polynomials

Vocabulary

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.

Example:

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 â€“1, and use the rules for multiplying signed numbers.

Example:

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.

Example:

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.