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Addition of Algebraic Fractions
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BEDMAS & Fractions
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Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
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Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
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Graphing Equations in Three Variables
Properties of Exponents
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Adding and Subtracting Fractions
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Factoring Polynomials by Finding the Greatest Common Factor
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Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
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Factoring Polynomials
Solving Quadratic Equations
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Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
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Arithmetic with Positive and Negative Numbers
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Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
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Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Percents
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Radicals
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
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Multiplication by 429
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Introduction to Fractions
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Factoring Special Quadratic Polynomials

WHAT TO DO: HOW TO DO IT:
If there is no common factor check for the two special types of factorable polynomials: a) difference of squares

b) perfect square trinomial

(a) difference of squares The difference of squares always factors to the sum and difference of the square roots of those squares. A2 − B2  = (A + B)(A − B)
Sometimes the factors themselves contain another factorable binomial -- difference of squares. i) (s 4 − t 4) = (s2 + t2)(s2 − t2)

= (s2 + t2)(s + t)(s − t)

Check for factorable binomial -- difference of squares.

Continue factoring to prime factors:

ii) x8 − y8 = (x4 + y4)(x4 - y4)

= (x4 + y4)(x2 + y2)(x2 - y2)

= (x4 + y4)(x2 + y2)(x + y)(x − y)

Factor to prime factors: iii) x16 - y16 = (x8 + y8)(x4 + y4)(x2 + y2)(x + y)(x - y)
b) perfect square trinomial
Perfect square trinomials must have the first and last terms be perfect squares and the last sign positive. If all of these conditions hold, check to see if the product of the square roots of the first term and the last term is the same as half the middle term or if the middle term is twice the cross product of the square roots.  i) 4x2 - 12x + 9 = (2x - 3)2

ii) 9x2 + 30x + 25 = (3x + 5)2

iii) 25x2 + 60x + 36 = (5x + 6)2

NOTE: if the last sign is not + or if the middle term is not twice the square root factors, the trinomial is not a perfect square trinomial and all must be examined by other criteria, such as the Grouping Number. a) 4x2 + 12x - 9

b) 4x2 - 13x + 9

c) 4x2 + 15x + 9

NOTE: If the trinomial isn’t immediately recognized as a perfect square trinomial, the best method is to treat it as “any trinomial” and use factor by grouping.
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