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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Factoring Special Quadratic Polynomials

⇒ Check for common factors and factor them out of the polynomial.


25ax3 - 40 abx2 + 15a2x2

5 ax2(5x - 8b + 3a)

If there is no common factor check for the two special types of factorable polynomials:


a) Difference of Squares (binomial)

b) Perfect Square Trinomial

(a) Difference of Squares (binomial)

The difference of squares always factors to the sum and difference of the square roots of those squares.

A2 − B2 = (A + B)(A − B)
i) Factor 4x2 − 9

Difference of Squares (binomial)

i) 4x2 − 9 =

(2x + 3)(2x − 3)

ii) Factor 9x2 − 25

Difference of Squares (binomial)

ii) 9x2 − 25 =

(3x + 5)(3x − 5)

b) Perfect Square Trinomial
Perfect square trinomials must have the first and last terms be perfect squares and the last sign positive. 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.
The "middle sign" is the "sign of the binomial".
∴ Factor the trinomial: 25x2 + 60x + 36 = (5x + 6) 2
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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