Warm Up W1D5 8/10/11 2. Solve: |4x+2|=5 8x-4 1. = |x+2|=15

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Warm Up W1D5 8/10/11 2. Solve: |4x+2|=5 8x-4 1. = 30 2 3. 5|x+2|=15 1. = 30 2 3. 5|x+2|=15 4. -5 ≤ 4u-6 ≤ 14 5. Simplify x2x=

Adding, Subtracting, Multiplying, and Dividing Polynomials August 10, 2011 Week 1 Day 5 EQ: How do we add, subtract, multiply, and divide polynomials?

Adding Polynomials Simplify: (2x+5y)+(3x-2y) 2x+5y+3x-2y 2x+3x+5y-2y Combining Like Terms and following Order of Operations (PEMDAS)

You Try! Simplify (3x3+3x2-4x+5)+(x3-2x2+x-4) Did you get 4x3+x2-3x+1?

You Try! Simplify (x3+5x2-2x)+(x3+3x-6)+(-2x2+x-2) Did you get 2x3+3x2+2x-8?

Subtracting Polynomials Simplify: (x3+3x2+5x-4)-(3x3-8x2-5x+6) X3+3x2+5x-4-3x3+8x2+5x-6 X3-3x3+3x2+8x2+5x+5x-4-6 -2x3+11x2+10x-10 Just like adding. Just remember: Distribute the negative!

You Try! Simplify (6x3-2x2+8x)-(4x3-11x+10) Did you get 2x3-2x2+19x-10?

BEFORE we multiply polynomials: Remember Rules of Exponents? Multiplying: ( x4)(x3) = (xxxx)(xxx) =xxxxxxx =x7 When we multiplying two numbers with the same base, we add our exponents. (x4)(x3) =x(4+3) =x7

Multiplying Polynomials Simplify: -3x(4x2-x+10) -3x(4x2)-3x(-x)-3x(10) -12x3+3x2-30x When multiplying one term by a multi-term polynomial, DISTRIBUTE!

You Try! Simplify 4x2 (4x3-x+8) Did you get 16x5-4x3+32x2?

Multiplying Polynomials Simplify: (x+3)(x+2) + + + x2+5x+6 When multiplying a two-term polynomial by a two-term polynomial, we FOIL or BOX! x2 2x 3x 6

You Try! Simplify (4x3-x)(x+8) Did you get 4x4+32x3-x2-8x?

Multiplying Polynomials Multiplying multi-term polynomial by another multi-term polynomial, it is similar to the FOIL method and distributing Simplify: (4x2-4x-7)(x+3) 4x3-4x2-7x+12x2-12x-21 4x3-4x2+12x2-7x-12x-21 4x3-+8x2-19x-21

You Try! Simplify (x+2)(x3+3x2+4x-17) Did you get x4+5x3+10x2-9x-34?

When dividing a polynomial by another polynomial, we Dividing Polynomials X2 - 2x + 4 When dividing a polynomial by another polynomial, we LONG DIVISION! 3x+1 3x3-5x2+10x+4 3x3-x2 +10x+4 -6x2 - 2x +4 12x+4 -6x2 12x

Together, let’s try to divide (4x4+3x3+2x+1) by (x2+x+2) We get 4x2-x-7+ x2+x+2

You try to divide (2x3-9x2+25) by (2x-5) Did you get x2-2x-5?

Applying to Other Applications What is the perimeter of the triangle? x2+5x+1 4x2+2x-7 7x2-2

Applying to Other Applications What is the area of the parallelogram? 2x2-7 3x2+x-5

Wrap Up What did we do today? When multiplying two terms with the same base, what do we do with the exponents? What is a method we use when multiplying two two-term polynomials? Add, Subtract, Multiply, and Divide Polynomials Multiply the exponents FOIL or BOX method

Worksheet: Adding, Subtracting, Multiplying, and Dividing Polynomials Homework Worksheet: Adding, Subtracting, Multiplying, and Dividing Polynomials Add/Subtract: #1-11 odd, 13a, 14, 15 Multiply/Divide: #2-16 even, 19-22 all, 28a