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Thursday 21st of November



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	Factoring Trinomials with Leading Coefficient 1
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	Writing a Rational Expression in Lowest Terms
	Solving Quadratic Inequalities with a Sign Graph
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	The Square of a Binomial
	Properties of Negative Exponents
	Inverse Functions
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	Combining Operations
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	Graphing Inequalities in Two Variables
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	Simple Trinomials as Products of Binomials
	Ratios and Proportions
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	Multiplying and Dividing Fractions 2
	Rational Numbers
	Difference of Two Squares
	Factoring Polynomials by Grouping
	Solving Equations That Contain Rational Expressions
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	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
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	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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Factoring Completely General Quadratic Trinomials

WHAT TO DO:	HOW TO DO IT:
Given a trinomial of type ax² Â± bx Â± c that has at least one common factor. Factor out all of the common factors then look at the remaining quadratic trinomial.	kÂ·(Ax² Â± Bx Â± C)
Given a general trinomial:	72x² − 60x − 28
Factor out common factor if there is one.	4(18x² − 15x − 7)
On Scratch Paper, look at polynomial inside (...):	18x² − 15x − 7
Use GN and Clue of Signs Multiply first and last coefficients:	GN 18Â·7 = 126
NOTE: Last sign is â€œ−â€ therefore Find all pairs of factors of 126 with difference of 15.
The largest factor of the pair gets sign of middle term, â€œ − â€ the other is positive:	− 21 and + 6
Rearrange polynomial using these values as coefficients of x	18x² − 21x + 6x − 7
Factor common factor from each group:	3x(6x − 7) + 1(6x −7)
Combine with first term factored out the complete factors of: 72x² - 60x - 28	4(3x + 1)(6x − 7) answer
Check by multiplying out: