Solving Quadratic Equations by Factoring

Equations that can be written in the form Ax² + Bx + C = 0

where a, b, and c are integers and a>0 are called quadratic equations . This form is called
the standard form.

The easiest way to solve quadratic equations is to factor (if possible) the polynomial on the left
side of the equation above . We then use the Zero- Product Theorem .

Zero- Product Theorem for any real numbers
a and b, if ab = 0, then a = 0 or b = 0.

Quadratic Equations :

1. x² – 3x – 4 = 0	This quadratic equation is in standard form.
2. A² = 6A – 9	This quadratic equation is not in standard form.
3. (x – 7)(x + 6) = –22	This is a quadratic equation not in standard form.
4. (x + 8)(x – 5) = 0	By the Zero-Product Theorem, the quadratic equation can be solved.
5. x(x – 14) = 0	This quadratic equation is in factored form and equal to zero ; it can be solved by using the Zero -Product Theorem.

To solve quadratic equations by factoring:

1. Put the equation into standard form.
2. Factor the polynomial .
3. Set each factor equal to zero.
4. Solve each of the first degree equations.

EXAMPLE 1:	2x² – 9x – 35 =0
Solution:	This is already in standard form, so we start by factoring.
Factor
Set each factor = 0
Solve each equation
The solution set is:
EXAMPLE 2:	a² = 6a – 9
Solution:	We first put this into standard form.
The equation is not in standard form	a² = 6a – 9
Put into standard form	a² – 6a + 9 = 0
Factor
Set each factor = 0
Solve each equation
The solution set is:	{3,3}
EXAMPLE 3:	(t – 7)(t + 6) = –22
Solution:	Multiple this out and put into standard form.
FOIL
Standard form
Factor
Set each factor = 0
Solve each equation	t = 5 t = –4
The solution set is:	{5,–4}
EXAMPLE 4:	Solve x(x – 14) = 0
Solution	The equation is in factored form and equal to zero . It can be solved by using the Zero-Product Theorem.
Factor
Set each factor = 0
The solution set is:	{0,14}

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of April 23rd you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
factoring and expanding expressions
finding LCM and GCF
(simplifying, rationalizing complex denominators...)
solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
solving a system of two and three linear equations (including Cramer's rule)
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
graphing general functions
operations with functions (composition, inverse, range, domain...)
simplifying logarithms
basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

2Checkout.com is an authorized reseller
of goods provided by Sofmath

"It really helped me with my homework. I was stuck on some problems and your software walked me step by step through the process..."

C. Sievert, KY

Sofmath
19179 Blanco #105-234
San Antonio, TX 78258

Phone: (512) 788-5675
Fax: (512) 519-1805