Transcript FACTORING PACKET

Factoring Part 3
FACTORING
#1: Take out the GCF
EX:
2x4 – 8x3 + 4x2 – 6x
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing.
Solution:
FACTORING
#1: Take out the GCF
EX:
2x4 – 8x3 + 4x2 – 6x
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing.
Solution:
2x(
)
FACTORING
#1: Take out the GCF
EX:
2x4 – 8x3 + 4x2 – 6x
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing.
Solution:
2x(x3
)
FACTORING
#1: Take out the GCF
EX:
2x4 – 8x3 + 4x2 – 6x
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing.
Solution:
2x(x3 – 4x2
)
FACTORING
#1: Take out the GCF
EX:
2x4 – 8x3 + 4x2 – 6x
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing.
Solution:
2x(x3 – 4x2 + 2x
)
FACTORING
#1: Take out the GCF
EX:
2x4 – 8x3 + 4x2 – 6x
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing.
Solution:
2x(x3 – 4x2 + 2x – 3)
FACTORING
#1: Take out the GCF
EX:
15xy2 – 10x3y + 25xy3
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing out.
Solution:
FACTORING
#1: Take out the GCF
EX:
15xy2 – 10x3y + 25xy3
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing out.
Solution:
5xy(
)
FACTORING
#1: Take out the GCF
EX:
15xy2 – 10x3y + 25xy3
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing out.
Solution:
5xy(3y
)
FACTORING
#1: Take out the GCF
EX:
15xy2 – 10x3y + 25xy3
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing out.
Solution:
5xy(3y – 2x2
)
FACTORING
#1: Take out the GCF
EX:
15xy2 – 10x3y + 25xy3
How to do it….
Find what is in common
in each term and put in
front. See what is left
over.
Check answer by
distributing out.
Solution:
5xy(3y – 2x2 + 5y2)
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….
Solution:
Make a table of factors of the
last number.
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….
Solution:
Make a table of factors of the
last number.
6
1 6
2 3
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….
Solution:
Make a table of factors of the
last number.
6
1 6
2 3
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….
Solution:
(x + 2)(x + 3)
Make a table of factors of the
last number.
6
1 6
2 3
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….
Solution:
(x + 2)(x + 3)
Check with FOIL
Make a table of factors of the
last number.
6
1 6
2 3
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….
Solution:
Make a table of factors of the
last number.
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….
Solution:
Make a table of factors of the
last number.
12
1
12
2
6
3
4
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….
Solution:
Make a table of factors of the
last number.
12
1
12
2
6
3
4
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….
Solution:
(x + 3)(x + 4)
Make a table of factors of the
last number.
12
1
12
2
6
3 4
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….
Solution:
(x + 3)(x + 4)
Check with FOIL.
Make a table of factors of the
last number.
12
1
12
2
6
3 4
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….
Solution:
Make a table of factors of the
last number.
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….
Solution:
Make a table of factors of the
last number.
6
1 6
23
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….
Solution:
Make a table of factors of the
last number.
6
1 6
23
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….
Solution:
(x + 6)(x + 1)
Make a table of factors of the
last number.
6
1 6
23
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….
Solution:
(x + 6)(x + 1)
Check with FOIL.
Make a table of factors of the
last number.
6
1 6
23
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
Make a table of factors of the
last number.
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
Make a table of factors of the
last number.
4
1 4
2 2
Pick the factors that add up to the
middle number.
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
Make a table of factors of the
last number.
4
1 4
2 2
Pick the factors that add up to the
middle number.
None of these work!
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
Make a table of factors of the
last number.
4
1 4
2 2
Pick the factors that add up to the
middle number.
None of these work!
TRY negatives
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
Make a table of factors of the
last number.
4
-1 -4
-2 -2
Pick the factors that add up to the
middle number.
None of these work!
TRY negatives
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
Make a table of factors of the
last number.
4
-1 -4
-2 -2
Pick the factors that add up to the
middle number.
None of these work!
TRY negatives
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
(x – 1)(x – 4)
Make a table of factors of the
last number.
4
-1 -4
-2 -2
Pick the factors that add up to the
middle number.
None of these work!
TRY negatives
FACTORING
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 - 5x + 4
How to do it….
Solution:
(x – 1)(x – 4)
Check with FOIL.
Make a table of factors of the
last number.
4
-1 -4
-2 -2
Pick the factors that add up to the
middle number.
None of these work!
TRY negatives
2
x
+ 6x + 5 =
2
x
+ 6x + 5 = (x + 5)(x + 1)
2
x
+ 10x + 16 =
2
x
+ 10x + 16 = (x + 2)(x + 8)
2
a
– 5a + 6 =
2
a
– 5a + 6 = (a – 2)(a – 3)
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 + 2x - 15
How to do it….
Solution:
Make a table of factors of the
last number.
Pick the numbers that add to be
the middle number.
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 + 2x - 15
How to do it….
Solution:
Make a table of factors of the
last number.
15
1 -15
3 -5
-1 15
-3 5
Pick the numbers that add up to
be the middle number.
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 + 2x - 15
How to do it….
Solution:
Make a table of factors of the
last number.
15
1 -15
3 -5
-1 15
-3 5
Pick the numbers that add up to
be the middle number.
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 + 2x - 15
How to do it….
Solution:
Make a table of factors of the
last number.
15
1 -15
3 -5
-1 15
-3 5
Pick the numbers that add up to
be the middle number.
(x + 5)(x – 3)
#2: Trinomials with a
leading coefficient of 1.
EX:
notice the signs
x2 + 2x - 15
How to do it….
Solution:
Make a table of factors of the
last number.
15
1 -15
3 -5
-1 15
-3 5
Pick the numbers that add up to
be the middle number.
(x + 5)(x – 3)
Check with FOIL.
2
y
+ 3y - 10 =
2
y
+ 3y - 10 =
10
2
y
+ 3y - 10 =
10
1 -10
2 -5
-1 10
-2 5
2
y
+ 3y - 10 =
10
1 -10
2 -5
-1 10
-2 5
2
y
+ 3y - 10 =
10
1 -10
2 -5
-1 10
-2 5
(x + 5)(x – 2)