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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