	Algebra Tutorials!

	Thursday 21st of November



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	Simplifying Radical Expressions Containing One Term
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	Multiplying and Dividing With Square Roots
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	Absolute Value Function
	Real Numbers and the Real Line
	Monomial Factors
	Raising an Exponential Expression to a Power
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	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
	Decimals
	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
	Equations

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Factoring Special Quadratic Polynomials

WHAT TO DO:	HOW TO DO IT:
⇒ 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.