Download Multiplying Polynomials

How to factor your
food and foil the
leftovers!
Summer McElman
Pi Day Project 2012
Multiplying Polynomials
 A polynomial consists of two or more numbers, variables,
or products with or without exponents.
• Ex) 5x+3, -2y-1, x²+3
 A standard form of multiplying polynomials would be
• (x+4)(x+2)
 To multiply polynomials three methods are possible
1. Algebra Tiles
2. Punnett Square
3. Foil
Algebra Tiles
 There are three different shapes of Algebra tiles and
each side is important. Colors represent positive and
negative and are usually used by the colors green(blue)
and red(black).
1
-1
x
x²
-x²
-x
Multiplying Algebra Tiles
 Ex) (x+3)(x+4)
1. Represent factors with tiles
2. Fill in spots to connect tiles
3. Trinomial is created
• x² + 7x + 12
x²
x
x
x
x
x
1
1
1
1
x
1
1
1
1
x
1
1
1
1
Practice Problem
1.
Your sister is making tuna sandwiches and she needs to know
the area of the bread in order to make enough tuna to cover it.
You measure the sides to be (x+2) and (x+4). What is the total
area?
x² + 6x + 8
x²
1x
1x
1x
1x
1x
1
1
1
1
1x
1
1
1
1
Punnett Square
 Ex) (x+5)(x+2)
1. Plug factors into punnett square
2. Multiply by rows
3. Simplify polynomial
x
5
x
x²
5x
2
2x
10
𝑥 2 + 5𝑥 + 2𝑥 + 10
𝑥 2 + 7𝑥 + 10
Practice Problem
1. Your brother is eating a block of cheese and you want
to the know the area of the section he bit off of. You
measure the sides to be (x+1) and (x+3). What is the
area of the bitten off cheese?
x
3
x
x²
3x
1
x
3
x² + 3x + x + 3
x² + 4x + 3
Foil
 Ex) (x+7)(x+3)
1. First: (x+7)(x+3) = (x)(x) = x²
x²+3x+7x+21
2. Outside: (x+7)(x+3) = (x)(3) = 3x
x²+10x+21
3. Inside: (x+7)(x+3) = (7)(x) = 7x
4. Last: (x+7)(x+3) = (7)(3) = 21
The Food Pyramid
GRAINS
VEGETABLES
FRUITS
OILS
MILK
MEAT & BEANS