Download Multiplying Binomials

Factoring
Factoring the Greatest Common Factor:
1) Find the GCF of the coefficients
2) Find the variable with the lowest exponent
3) Divide each term by the GCF
a. Divide the coefficients
b. Subtract the exponents
Examples on how to find the GCF:
1) 24x5 – 60x3 + 48x2
2) 15x7 + 30x5 + 27x4
3) 12x9 + 16x3 – 28
GCF: 12x2
GCF: 3x4
GCF: 4
1) 14x8 + 7x6 – 28x3
2) 12x8 + 30x4 + 18
3) 22x7 + 18x3 + 6x
GCF:
GCF:
GCF:
TRY THESE:
Examples on factoring out the GCF:
1) 12x7 + 4x3 – 20x2
GCF: 4x2
12x7 + 4x3 – 20x2
4x2 4x2 4x2
Divide each term by GCF
Answer: 4x2(3x5 + x – 5)
2) 15x7 + 30x5 + 27x4 GCF: 3x4
15x7 + 30x5 + 27x4
3x4
3x4
3x4
Divide each term by GCF
Answer: 3x4(5x3 + 10x + 9)
Try these:
1) 24x9 + 12x5 + 18x3
Answer:
(
2) 16x4 + 18x3 – 20x
GCF:
)
Answer:
(
)
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Factoring out GCFs
Name:______________________
Factor:
1) 9x4 – 12x10 + 18x7
2) 16x8 + 4x7 – 2x
3) 10x2 + 5x – 20
4) 18x6 – 24x7 + 42x16
5) 30a4 – 2a3 + 6a2
6) 64x9 – 16x7 + 24x8
7) 12x10 – 24x4 + 48x3
8) 15x5 – 21x4 + 3x3
9) 7x10 – 6x4 + 9x2
10) 16x10 – 8x7 + 56
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Factoring Trinomials
1) List the last term (represents the product)
2) List the middle term (represents the sum)
3) Find two numbers that multiply to get the last term and add/subtract to the middle term
4) Write these two numbers in the format (x ± #)(x ± #)
Examples:
1) x2 + 8x + 12
Ask what factors of 12 add to +8
Factors
2) x2 + 3x – 10
Factors
1*12
What factors of 10 subtract to get +3
1*10
2*6
2*5
Answer: (x + 2)(x + 6)
3*4
Answer: (x – 2)(x + 5)
___________________________________________________________________________
Try these:
1) x2 + 5x + 6
2) x2 + 10x – 24
3) x2 – 10x + 21
(x
)(x
)
(x
)(x
)
(x
)(x
)
____________________________________________________________________________
4) x2 – 9x + 18
5) x2 – 12x – 13
6) x2 + 8x + 15
(x
)(x
)
(x
)(x
)
(x
)(x
)
______________________________________________________________________________
7) x2 + 3x – 10
8) x2 – 4x – 12
9) x2 + 19x – 20
______________________________________________________________________________
10) x2 – 3x – 18
11) x2 – 12x + 20
12) x2 + 8x + 12
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Factoring trinomials practice
1) x2 + 25x + 24
2) a2 – 14a + 63
3) y2 + 7y – 18
4) x2 – 13x + 22
5) x2 – 2x – 35
6) m2 + 18m – 40
7) y2 + 8y + 7
8) x2 + x – 42
9) x2 – 12x + 20
10) x2 + 14x + 33
11) a2 – 27 + 50
12) y2 + 2y – 15
13) x2 – 7x + 12
14) x2 – 3x – 8
15) m2 + 4m – 21
16) y2 + 8y + 16
17) x2 + 3x – 28
Bonus: 4x7 – 12x6 – 40x5
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Special Case Factoring:
Difference of Two Squares:
a2 – b2 = (a + b)(a – b)
Find the square root of “a” and the square root of “b”
Examples:
1) x2 – 81
(x + 9)(x – 9)
2) x2 – 49
(x + 7)(x – 7)
3) 25y2 – 16z2
(5y + 4z) (5y – 4z)
Try these:
1) b2 – 9
2) r2 – 64
3) 4a2 – 36b2
Solving equations by Factoring
1) Factor the trinomial by finding the numbers that multiply to the third term and add to the
second term
2) Find the zero’s of x
Examples:
1) x2 – 10x + 16 = 0
2) x2 + x – 12 = 0
3) x2 – 25 = 0
(x – 2)(x – 8) = 0
(x – 3)(x + 4) = 0
(x + 5)(x – 5) = 0
x = 2 or x = 8
x = 3 or x = -4
x = -5 or x = 5
Try these:
1) x2 – 9x – 10 = 0
2) x2 + 8x + 16 = 0
3) x2 – 100 = 0
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Solving Equations by Factoring
1) (k + 1) (k + 3) = 0
2) (a – 6)(a + 9) = 0
3) (x – 9)(x – 6) = 0
4) x2 – 11x + 24 = 0
5) n2 + 7x + 10 = 0
6) m2 – 10m + 24 = 0
7) a2 + 3a – 18 = 0
8) t2 – 81 = 0
9) b2 – 49 = 0
Hint: Factor out the GCF
10) 2x2 – 8x = 0
11) 3x5 + 12x4 = 0
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Factoring Test Review
Name:__________________
Rules to Factoring:
1) Check for GCF first
2) Factor with two ( )
- If: Trinomial, then ask what factors of the last term add or sub to get middle term
- If Binomial: then difference of two squares a2 – b2 = (a + b)(a – b)
1) x2 – 7x + 12
2) x2 – 121
3) x2 + 9x – 10
4) 12x5 – 20x9 + 28x3
5) a2 + 10a + 24
6) 9x2 – 49
7) 3x2 – 6x – 45
8) x2 + x – 42
9) x2 – 4x – 32
10) 21x5 + 35x3 – 14x
11) 8x2 - 24x – 16
12) b2 + 7b + 10
13) x7 + 4x6 – 12x5
14) m2 – 100
15) y2 – 13y + 12
Solve by Factoring
16) x2 – x – 30 = 0
17) a2 – 16 = 0
19) s2 – 3s – 10 = 0
20) x2 – 144 = 0
18) y2 + 3y – 28 = 0
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