2
2
2
2
40
8
12
x
y
x
y
x
±
±
4 is a factor of all three terms
2
x
is a factor of all three terms.
Divide each term by the
2
4
x
. I think of what I need to
multiply
2
4
x
by to get each of the original terms of the
2
2
2
2
40
8
12
x
y
x
y
x
±
±
You can check by multiplying.
Factoring polynomials of the form x
²
+ bx +c
factors of "c" whose sum is "b"
write those numbers (x …)(x…)
After we do an example we can see why it works by checking.
²
³
2
5
3
5
2
3
±
´
x
x
x
²
³
3
4
5
2
3
10
25
15
2
5
3
5
x
x
x
x
x
x
±
´
±
´
²
³
10
2
3
4
2
2
±
±
y
y
x

4.2 Factoring and Solving by Factoring
page 150
By Will Tenney
3. Factor
Steps
Reasons
b is 5 and c is 6
Look for the factors of "c" whose sum is "b".
List factors of 6
1·6,
-1·(-6),
2·3,
-2·(-3)
2 and 3 have a sum of 5
Write those numbers after the (x …)(x …)
When we check by multiplying, we see why the sum of the numbers is 5 and the
product is 6.
4. Factor:
Steps
Reasons
b is
–
5 and c is
–
24
List factors of -24
–
2·12
,
–
3·8,
3·(
–
8)
3 and
–
8 have a sum of
–
24
Look for the factors of "c" whose sum is "b".
Write those numbers after the (x …)(x …)
5. Factor:
7
3
2
´
´
x
x
Steps
Reasons
7
3
2
´
´
x
x
b is 3 and c is 7
List factors of 7
1·7,
–
1·(
–
7)
Look for the factors of "c" whose sum is "b".
None of the factors of 7 add up to 3
So,
7
3
2
´
´
x
x
does not factor. We can also say that
7
3
2
´
´
x
x
is prime.
6
5
2
´
´
x
x
6
5
2
´
´
x
x
²
³²
³
3
2
´
´
x
x
²
³²
³
6
5
6
2
3
·
3
2
2
´
´
´
´
´
´
´
x
x
x
x
x
x
x
x
24
5
2
±
±
x
x
24
5
2
±
±
x
x
²
³²
³
3
8
´
±
x
x
In the FOIL we will always get x·x
2x + 3x = 5x
We needed the sum to be 5
2·3 = 6
We only tried factors of 6

4.2 Factoring and Solving by Factoring
page 151
By Will Tenney
6. Factor:
Steps
Reasons
First factor out the common factor.
The factors of
–
3 whose sum is
–
2 are
–
3 and 1.
Keep the common factor of 6x.
Factoring polynomials of the form ax
²
+ bx + c by Guess and Check:
We are doing FOIL backwards.
ax
²
is coming from the first terms and c is coming
from the last terms. We can check all possibilities that will give us
ax
²
and
c
. Then
we check the FOIL to see if we have the right
bx
term.
Examples
7. Factor 2x
²
+ 7x + 3
Steps
Reasons
2x
²
must factor into 2x and x in the first two terms.
Check:
The factors of 3 are 1,3 and . Try them in both possible
orders. They would not be negative because the middle
term 7x is positive.
If you check the FOIL the answer is the second choice.
Check:
Here we are guessing 2x and x for the first part of the factors because they will
give us 2x
²
in the FOIL. We guess 1 and 3 for the second part of the factors
because they will give us 3 in the FOIL. We have to try the various combinations
and do the FOIL to see which combination works.

#### You've reached the end of your free preview.

Want to read all 433 pages?

- Summer '19
- Math, Statistics, Algebra, Sets