Free Algebra Tutorials!

 Home Point Arithmetic Operations with Numerical Fractions Multiplying a Polynomial by a Monomial Solving Linear Equation Solving Linear Equations Solving Inequalities Solving Compound Inequalities Solving Systems of Equations Using Substitution Simplifying Fractions 3 Factoring quadratics Special Products Writing Fractions as Percents Using Patterns to Multiply Two Binomials Adding and Subtracting Fractions Solving Linear Inequalities Adding Fractions Solving Systems of Equations - Exponential Functions Integer Exponents Example 6 Dividing Monomials Multiplication can Increase or Decrease a Number Graphing Horizontal Lines Simplification of Expressions Containing only Monomials Decimal Numbers Negative Numbers Factoring Subtracting Polynomials Adding and Subtracting Fractions Powers of i Multiplying and Dividing Fractions Simplifying Complex Fractions Finding the Coordinates of a Point Fractions and Decimals Rational Expressions Solving Equations by Factoring Slope of a Line Percent Introduced Reducing Rational Expressions to Lowest Terms The Hyperbola Standard Form for the Equation of a Line Multiplication by 75 Solving Quadratic Equations Using the Quadratic Formula Raising a Product to a Power Solving Equations with Log Terms on Each Side Monomial Factors Solving Inequalities with Fractions and Parentheses Division Property of Square and Cube Roots Multiplying Two Numbers Close to but less than 100 Solving Absolute Value Inequalities Equations of Circles Percents and Decimals Integral Exponents Linear Equations - Positive and Negative Slopes Multiplying Radicals Factoring Special Quadratic Polynomials Simplifying Rational Expressions Adding and Subtracting Unlike Fractions Graphuing Linear Inequalities Linear Functions Solving Quadratic Equations by Using the Quadratic Formula Adding and Subtracting Polynomials Adding and Subtracting Functions Basic Algebraic Operations and Simplification Simplifying Complex Fractions Axis of Symmetry and Vertices Factoring Polynomials with Four Terms Evaluation of Simple Formulas Graphing Systems of Equations Scientific Notation Lines and Equations Horizontal and Vertical Lines Solving Equations by Factoring Solving Systems of Linear Inequalities Adding and Subtracting Rational Expressions with Different Denominators Adding and Subtracting Fractions Solving Linear Equations Simple Trinomials as Products of Binomials Solving Nonlinear Equations by Factoring Solving System of Equations Exponential Functions Computing the Area of Circles The Standard Form of a Quadratic Equation The Discriminant Dividing Monomials Using the Quotient Rule Squaring a Difference Changing the Sign of an Exponent Adding Fractions Powers of Radical Expressions Steps for Solving Linear Equations Quadratic Expressions Complete Squares Fractions 1 Properties of Negative Exponents Factoring Perfect Square Trinomials Algebra Solving Quadratic Equations Using the Square Root Property Dividing Rational Expressions Quadratic Equations with Imaginary Solutions Factoring Trinomials Using Patterns
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Factoring quadratics

## Introduction

On this leaflet we explain the procedure for factoring quadratic expressions such as x +5 x +6.

## 1. Factoring quadratics

You will find that you are expected to be able to factorize expressions such as x + 5 x + 6.

First of all note that by removing the brackets from

( x + 2)( x + 3)

we find ( x + 2)( x + 3) = x + 2 x + 3 x + 6 = x+ 5 x + 6

When we factorize x + 5 x + 6 we are looking for the answer ( x + 2)( x + 3).

It is often convenient to do this by a process of educated guesswork and trial and error.

Example

Factorize x + 6 x + 5.

Solution

We would like to write x + 6 x + 5 in the form

First note that we can achieve the x term by placing an x in each bracket:

The next place to look is the constant term in x+6 x +5, that is, 5. By removing the brackets you will see that this is calculated by multiplying the two numbers in the brackets together. We seek two numbers which multiply together to give 5. Clearly 5 and 1 have this property, although there are others. So

x + 6 x +5 = ( x + 5)( x + 1)

At this stage you should always remove the brackets again to check.

The factors of x+ 6 x + 5 are ( x + 5) and ( x + 1).

Example

Factorize x - 6 x + 5.

Solution

Again we try to write the expression in the form

x-6 x + 5 =

And again we seek two numbers which multiply to give 5. However this time 5 and 1 will not do, because using these we would obtain a middle term of +6 x as we saw in the last example. Trying 5 and 1 will do the trick.

x - 6 x +5 = ( x - 5)( x - 1)

You see that some thought and perhaps a little experimentation is required.

You will need even more thought and care if the coefficient of x, that is the number in front of the x, is anything other than 1. Consider the following example.

Example

Factorize 2 x + 11 x + 12.

Solution

Always start by trying to obtain the correct x term:

We write

2 x + 11 x +12 =

Then study the constant term12. It has a number of pairs of factors, for example 3 and 4, 6 and 2 and so on. By trial and error you will find that the correct factorization is

2 x + 11 x + 12 = (2 x + 3)( x + 4)

but you will only realize this by removing the brackets again.

All Right Reserved. Copyright 2005-2018