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Transcript
Factoring Trinomials
of the form ax2+bx+c with a =1.
Dr. Marcia L. Tharp
How to factor a trinomial of the form
ax2+bx+c when a=1
To factor a trinomial means to write it as a
product of two binomials.
For example x2+6x+8= (x+2) (x+4) two binomials
Remember we can use F.O.I. L. to multiply out
(x+2) (x+4) we get:
Adding the middle two terms you get
X2+6x+8
To get this trinomial into its factored form we use
F.O.I. L. in Reverse on x2+ 6x+8.
Remember that the FIRST term x2 came from its factors x (x).
So these two factors become the
first terms in each binomial.
Remember that the LAST term in each binomial came
from factors of the LAST term 8 in x2+ 6x+8
So 8 breaks down to 1(8) or 2(4). We need to choose which
pair of factors 1 and 8 or 2 and 4 we want to become the last
terms in each binomial
To do this we look at the middle terms of
x2+2x+4x+8.
When we use F.O. I. L. to multiply the
OUTSIDE and INSIDE terms in (X+2) (x+4)
The inside and outside products are 2x and 4x.
Their sum is 6x.
So we are looking for factors of 8 (the constant term)
that add to 6 to get the coefficient of the middle term
in
x2+ 6x+8.
Lets make a table to organize what we know.
We use a table to find two factors of 8 who sum to 6
the coefficient of the middle term in x2+6x+8.
Factors of 8
Sums of These Factors
1 and 8
1+8=9
2 and 4
2+4=6
So 2 and 4 have a sum of 6 and a product of 8.
So these are the factors of 8 we use as the last terms
of the binomial (x+__)(x+__).
Therefore
x2+6x+8= (x+2) (x+4)
Interactive FOIL Exploration
Print this page.
First get the Live Math Plug in at:
http://www.livemath.com/download/
Be sure to download the plug in for your
browser Internet Explorer or Netscape.
Next click on the link to the Live Math
Exploration and follow the directions in it.
http://www.tcc.edu/VML/Mth03/TRINOM/trinom3.htm
Finally click the back button on your browser to come
back to this lesson. If for some reason this page does
not work click back until you get to this presentation
ignore the link and click past this page.
Review
To Factor A Trinomial ax2+bx+c when a=1
Print this page.
1) Factor x2 into x (x).
2) Find two numbers who are factors of the last term
(constant term), c, and whose sum equals the coefficient of the
middle term (x-term) b.
3) Use the two numbers found in the above step, including their
signs, to write the trinomial in factored form. The trinomial in
factored form will be:
(X + a number) (X + a number)
Now go on to the practice problems.
Practice Problems
Try this practice.
Factor each trinomial below.
1)
x2+7x+12
answer
2)
x2-6x+8
answer
3)
x2-18x+80
answer
4)
x2-2x-80
answer
5)
b2-11b+18
answer
6)
x2+8xy+15y2 answer
Now click on the door to go on to
How to factor the form ax2+bx+c with a>1