|
2.04 Factoring Trinomials
Basic
Algebra: One Step at a Time. Pages
147-156: # 74, 83, 89
Dr. Robert J. Rapalje
Seminole Community College
Sanford, FL 32773
To see
Section 2.04, with
detailed explanations, examples, exercises, and answers,
click here!
p. 154: 74.
SOLUTION:
Notice that this is a
trinomial
since it has three terms. This can be factored using
F
OI
L (or actually
maybe it should be written F
L OI
).
In this case, the
First times First is obviously
x times
x.
The
Last times Last
must be two numbers whose product is
 .
Since the sign is negative,
this means that you must use opposite
signs for the two numbers. The
difference
between the two numbers must be the
middle term which is
 .
In other words, find two numbers whose product is
 and
whose difference
is
.
Can you think of it? If so, you can go ahead and put it down. If you can’t
think of it, then start with 1, and list all of the numbers that divide into
like
this:
After this, 7 does not divide
evenly into
.
Neither does 8 or 9. Then the next number would be 10, and
 is
the reverse of
.
This means that you have all the combinations.
Now, look at the list above, and
see which combination of numbers would have a difference of
.
That would be or
In order to make the middle term
come out to  ,
use
 times
 .
Of course,
 is
equally correct!!
p. 154: 83.
SOLUTION:
Notice that this is a
trinomial
since it has three terms. This can be factored using
F
OI
L (or actually
maybe it should be written F
L OI
).
In this case, the
First times First is obviously
x times
x.
The
Last times Last
must be two numbers whose product is
 .
Since the sign is negative,
this means that you must use opposite
signs for the two numbers. The
difference
between the two numbers must be the
middle term which is
.
In other words, find two numbers whose product is
 and
whose difference
is
 .
Can you think of it? If so, you can go ahead and put it down. If you can’t
think of it, then start with 1, and list all of the numbers that divide into
like
this:
After this, 5 does not divide
evenly into
.
Neither does 6. Then the next number would be 7, and
 is
the reverse of
.
This means that you have all the combinations.
Now, look at the list above, and
see which combination of numbers would have a difference of
.
That would be
or
In order to make the middle term
 ,
use
 times
 .
Of course,
 is
equally correct!!
p. 154: 89.
SOLUTION:
Notice that this is a
trinomial
since it has three terms. This can be factored using
F
OI
L (or actually
maybe it should be written F
L OI
).
In this case, the First times First is obviously
x times
x.
The
Last times Last
must be two numbers whose product is
 .
Since the sign is negative,
this means that you must use opposite
signs for the two numbers. The
difference
between the two numbers must be the
middle term which is
 .
In other words, find two numbers whose product is
 and
whose difference
is
.
Can you think of it? If so, you can go ahead and put it down. If you can’t
think of it, then start with 1, and list all of the numbers that divide into
like
this:
After this, 6, 7, 8, and 9 do not
divide evenly into
,
and the next number would be is
the reverse of
.
This means that you have all the combinations.
Now, look at the list above, and
see which combination of numbers would have a difference of
.
That would be
or
In order to make the middle term
 ,
use
 times
 .
Of course,
 is
equally correct!!
Return
to main page Return
to Basic Algebra
Math in Living
C
O
L O
R
!!
|
: View Source, Show