	Algebra Tutorials!

Thursday 21st of November



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	Calculations with Negative Numbers
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	Roots - Radicals 1
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	Factoring Trinomials with Leading Coefficient 1
	Writing Linear Equations Using Slope and Point
	Simplifying Expressions with Negative Exponents
	Solving Equations 3
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	Collecting Like Terms
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	Power of a Quotient Property of Exponents
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	Solving Linear Systems of Equations by Elimination
	The Quadratic Formula
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	Polar Form of a Complex Number
	Solving Quadratic Equations
	Simplifying Complex Fractions
	Algebra
	Common Logs
	Operations on Signed Numbers
	Multiplying Fractions in General
	Dividing Polynomials
	Polynomials
	Higher Degrees and Variable Exponents
	Solving Quadratic Inequalities with a Sign Graph
	Writing a Rational Expression in Lowest Terms
	Solving Quadratic Inequalities with a Sign Graph
	Solving Linear Equations
	The Square of a Binomial
	Properties of Negative Exponents
	Inverse Functions
	fractions
	Rotating an Ellipse
	Multiplying Numbers
	Linear Equations
	Solving Equations with One Log Term
	Combining Operations
	The Ellipse
	Straight Lines
	Graphing Inequalities in Two Variables
	Solving Trigonometric Equations
	Adding and Subtracting Fractions
	Simple Trinomials as Products of Binomials
	Ratios and Proportions
	Solving Equations
	Multiplying and Dividing Fractions 2
	Rational Numbers
	Difference of Two Squares
	Factoring Polynomials by Grouping
	Solving Equations That Contain Rational Expressions
	Solving Quadratic Equations
	Dividing and Subtracting Rational Expressions
	Square Roots and Real Numbers
	Order of Operations
	Solving Nonlinear Equations by Substitution
	The Distance and Midpoint Formulas
	Linear Equations
	Graphing Using x- and y- Intercepts
	Properties of Exponents
	Solving Quadratic Equations
	Solving One-Step Equations Using Algebra
	Relatively Prime Numbers
	Solving a Quadratic Inequality with Two Solutions
	Quadratics
	Operations on Radicals
	Factoring a Difference of Two Squares
	Straight Lines
	Solving Quadratic Equations by Factoring
	Graphing Logarithmic Functions
	Simplifying Expressions Involving Variables
	Adding Integers
	Decimals
	Factoring Completely General Quadratic Trinomials
	Using Patterns to Multiply Two Binomials
	Adding and Subtracting Rational Expressions With Unlike Denominators
	Rational Exponents
	Horizontal and Vertical Lines

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Dividing Polynomials

Dividing a Polynomial by a Polynomial

Example

Use long division to find (6x³ + 7x² + 4x - 2) Ã· (2x + 1)

Solution Step 1 Write the problem in long division form.	Algebra
The terms of each polynomial are in descending order.
Step 2 Divide the first term of the dividend by the first term of the divisor.		Hereâ€™s a long division problem from arithmetic to help you see the similarities between the algebra and the arithmetic.
Divide 6x³ by 2x to get 3x². Write 3x² in the quotient line above 7x², the x²-term of the dividend.
Step 3 Multiply the divisor by the term you found in Step 2.
Multiply (2x + 1) by 3x² to get 6x³ + 3x².
Step 4 Subtract the expression you found in Step 3 from the dividend.
Subtract (6x³ + 3x²) from (6x³ + 7x²). The result is 4x².
Step 5 Bring down the next term from the dividend.
Write + 4x to the right of 4x².
Step 6 Repeat Steps 2 through 5 until the degree of the remainder is less than the degree of the divisor.
Divide 4x² by 2x to get 2x. Write 2x in the quotient line. Multiply (2x + 1) by 2x to get 4x² + 2x. Subtract (4x² + 2x) from (4x² + 4x). The result is 2x. Write -2 to the right of 2x.
Divide 2x by 2x to get 1. Write +1 in the quotient line. Multiply (2x + 1) by 1 to get 2x + 1. Subtract (2x + 1) from (2x - 2). The result is -3.
The degree of the remainder, -3, is less than the degree of the divisor, 2x + 1. So we stop.
Step 7 Write the quotient. The quotient is:		Quotient is