# Factoring Polynomials of the Form ax^2+bx+c

Chapter 8.3--Factoring Polynomials of the form
Factoring polynomials of the form is usually d one in one of two ways .

Part 1 Factoring by trial (and error)

Given the trinomial find the factors of both a and c . Then check to see which products of these factors add up to b .

Question 7: Factor
Factors of

Now test all the combinations of binomial pairs (until you get one that works).

In this case the last one we tried worked. We could have shortened our trials if we noticed that since the middle term of the problem is negative , we wouldn't have to test the positive factors .

Question 6 Now you try this one:
Factors of

Now test all the combinations of binomial pairs (until you get one that works).

Question 53: Factor

Take out the common factor first:

The factors are

Question 38:

So the factors are

Part 2 Factoring by grouping

 Algorithm: In the trinomial multiply ac . Then find all the factors of ac .Find the pair r,s that add up to b , and rewrite the trinomial as .  Finally factor this by grouping.

Question 78: Factor

All the factors of are:
1,40 sum is 41
2,20sumis22
4,10 sum is 14
5,8 sum is 13
I used "sum" because the last coefficient is positive
Use minus because the middle coefficient is negative

Now factor by grouping:

Question 71 Now you do this one: Factor
ac = 15
Write down all the factors of ac =15
1,15 their sum is 16 (This is what we want.)
3,5 their sum is 8

factor by grouping.

Question 107: Factor
Factor out the common factor first:

Multiply 2 and 5
Factors of 10 are
1,10 their difference is 9
2,5 their difference is 3

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

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 25th 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!