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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….Make a table of factors of the
last number.
Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3Pick the factors that add up to the middle number.
Solution:
(x + 2)(x + 3)
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 5x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3Pick the factors that add up to the middle number.
Solution:
(x + 2)(x + 3)
Check with FOIL
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….Make a table of factors of the
last number.
Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….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.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….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.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….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.
Solution:
(x + 3)(x + 4)
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 12
How to do it….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.
Solution:
(x + 3)(x + 4)
Check with FOIL.
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….Make a table of factors of the
last number.
Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3
Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3
Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3
Pick the factors that add up to the middle number.
Solution:
(x + 6)(x + 1)
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX:
x2 + 7x + 6
How to do it….Make a table of factors of the
last number. 6
1 6
2 3
Pick the factors that add up to the middle number.
Solution:
(x + 6)(x + 1)
Check with FOIL.
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number.
Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number. 4
1 4
2 2Pick the factors that add up to the middle number.
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number. 4
1 4
2 2Pick the factors that add up to the middle number.
None of these work!
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number. 4
1 4
2 2Pick the factors that add up to the middle number.
None of these work!
TRY negatives
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number. 4
-1 -4
-2 -2Pick the factors that add up to the middle number.
None of these work!
TRY negatives
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number. 4
-1 -4
-2 -2Pick the factors that add up to the middle number.
None of these work!
TRY negatives
Solution:
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number. 4
-1 -4
-2 -2Pick the factors that add up to the middle number.
None of these work!
TRY negatives
Solution:
(x – 1)(x – 4)
FACTORING
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 - 5x + 4
How to do it….Make a table of factors of the
last number. 4
-1 -4
-2 -2Pick the factors that add up to the middle number.
None of these work!
TRY negatives
Solution:
(x – 1)(x – 4)
Check with FOIL.
x2 + 6x + 5 =
x2 + 6x + 5 = (x + 5)(x + 1)
x2 + 10x + 16 =
x2 + 10x + 16 = (x + 2)(x + 8)
a2 – 5a + 6 =
a2 – 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….Make a table of factors of the
last number.
Pick the numbers that add to be the middle number.
Solution:
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 + 2x - 15
How to do it….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.
Solution:
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 + 2x - 15
How to do it….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.
Solution:
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 + 2x - 15
How to do it….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.
Solution:
(x + 5)(x – 3)
#2: Trinomials with a leading coefficient of 1.
EX: notice the signs
x2 + 2x - 15
How to do it….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.
Solution:
(x + 5)(x – 3)
Check with FOIL.
y2 + 3y - 10 =
y2 + 3y - 10 = 10
y2 + 3y - 10 = 10
1 -10
2 -5
-1 10
-2 5
y2 + 3y - 10 = 10
1 -10
2 -5
-1 10
-2 5
y2 + 3y - 10 = 10
1 -10
2 -5
-1 10
-2 5
(x + 5)(x – 2)
