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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
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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