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Name______________________________________ Block ________________
Date
11-13-13
Warmup-- List the first 15 perfect squares. Example: 12 = 1.
Three different methods of Multiplying Polynomials by Polynomials
FOIL = Firsts, Outers, Inners, Lasts
(3x + 4)(2x – 7)
6x2 – 21x + 8x – 28
6x2 – 13x – 28
(3x + 4)(2x – 7)
Double
Distribution (3x + 4)(2x – 7)
(3x + 4)(2x – 7) =
3x (2x – 7) = 6x2 –21x
+ 4 (2x – 7) =
8x – 28
6x2 – 13x – 28
Box Method (3x + 4)(2x – 7)
3x
4
2x -7
6x2 -21x
8x
-28
6x2 – 21x
+ 8x -28
6x -13x – 28
2
Practice A – Multiply the following polynomials using the box method.
1. (x – 4)(2x + 9)
2. (-3y – 4)(2y + 2)
4.
(6x – 3)(2x2 + 4x – 3)
5. (5y + 4) (8y – 12)
3.
(8 + w)(-10 – 3w)
6. (3p + 4) (2p2 +4p– 9)
Factors are numbers that are _____________________________ together. They divide __________________
into a product.
Practice B – List all of the factors for each number. Label each number Prime or composite
1.
14
2. 11
3. 48
4. 64
5. 72
6. 44
Prime Numbers – numbers ___________________ than one, and have only factors of ______ and itself
Composite Numbers – numbers __________________ than one and have more than ________ factors
Greatest Common Factor – The largest number that divides ____________________ into ________ or more
numbers
To Find GCF in calculator – press ________________, slide to ______________, go down to ______________
Can be used to find the gcf of any two positive numbers.
Practice C – Find the GCF
1. 14, 11
2. 48, 64
3. 11, 44
4. 64 , 72
5.
44, 14
Find GCF of polynomials – find the gcf of the ________________________________
____________________ the________________________ they have in common.
Select the __________________ __________________ for each variable
Practice D – find the GCF
1. 36x2y + 54xy2
2. 33y3z + 69y2z
4. 24x2y + 56x2yz
5. 34x6y3 + 68x3 y4
Factoring—taking a ________________________________ and splitting it up into its ___________________
Practice E – Factor the polynomial. You should end up with a monomial multiplied to a polynomial
1. 3x2 + 21x
2. 12x2 + 54x
7. 8x4 – 32x2
8. 12y5 + 30y3
Practice F – Find the area of each
1.
5x + 2
2.
2x – 3
3y3
3. 27x3 – 36x2
9. 16z9 – 24z5
4. x2 + 2x
5. 7x4 – 14x2
6. 2x2 + 16x
10. 15x – 18x7
11. 21x4 + 14x
12. 30g4 – 10g
6d2
3.
5x4
4.
5.
2d2
6y4
4g4 h3
Practice G – Find the perimeter or circumference
1.
3x2 + 4
2.
5g– 3
find area of shaded
3.
x2 – 1
4d2+2
4.
4x3
6x2
6x3
Practice H – Find the volume
1.
2.
3.
8y
2y
15y
5x + 5
3x
4x