Algebra Tutorials!
About Us


Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
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
Equivalent Fractions
Multiplying Polynomials
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
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
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
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
Plotting a Point
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
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
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
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
Try the Free Math Solver or Scroll down to Tutorials!












Please use this form if you would like
to have this math solver on your website,
free of charge.

Factoring Special Quadratic Polynomials

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.
Copyrights © 2005-2024
Monday 22nd of July