 # 3.1 Adding, Subtracting and Multiplying Polynomials 11/26/2012.

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3.1 Adding, Subtracting and Multiplying Polynomials 11/26/2012

Example 1 Add Polynomials Vertically a. Add and 2x 32x 3 x9 + 4x 24x 2 + – x 3x 3 5x5x1 6x 26x 2 – + – 3x 33x 3 4x4x8 2x 22x 2 – ++ SOLUTION 2x 32x 3 x9 + 4x 24x 2 + – x 3x 3 5x5x1 6x 26x 2 – + – + a.

Example 1 Add Polynomials Horizontally b. Add and 5x 25x 2 2x2x + 4x 24x 2 3 7x7x – + b. 5x 25x 2 2x2x + 4x 24x 2 3 7x7x – + () + () 5x 25x 2 4x 24x 2 + 2x2x 3 7x7x – + () + () = 9x 29x 2 3 5x5x – + = Group like terms. Combine like terms.

Example 2 Subtract Polynomials SOLUTION Align like terms, then add the opposite of the subtracted polynomial. 6x 36x 3 7x7x12 x 2x 2 – + – 3x 33x 3 9x9x 4x 24x 2 + + () – 6x 36x 3 7x7x x 2x 2 – + – 3x 33x 3 9x9x 4x 24x 2 + ––– 3x 33x 3 2x2x 5x 25x 2 –– –

Example 3 Use the Distributive Property Simplify the expression. 2x 22x 2 5 x – + x 2x 2 7 3x3x + – ()() + 42 14 6x6x + 8x 28x 2 20 4x4x – = – Use distributive property. ++ 2x 22x 2 6x6x + 8x 28x 2 4x4x 2x 22x 2 – = Group like terms. () + () ++ () 20 – 14 10x 2 = Combine like terms. 2x2x + 6 + a.

Example 3 Use the Distributive Property = Use distributive property. x 4x 4 x 3x 3 ++ x 2x 2 x + x 3x 3 x 2x 2 x + –– 1 – = Group like terms. x 4x 4 x 3x 3 ++ 1 – () x 3x 3 – x 2x 2 + () x 2x 2 – x ( x ) – = Combine like terms. x 4x 4 2x2x + 1 –

Review: Product of Powers: Ex. x 2 x 5 = x x x x x x x = x 7 = x 2+5 In general: a ma n = a m+n

Example 4 Multiply Polynomials Vertically Find the product. () x 2x 2 4x4x7 – + () 2x – SOLUTION Line up like terms vertically. Then multiply as shown below. x 2x 2 4x4x7 – + 2x – × 2x 22x 2 8x8x+14 –– Multiply by 2. x 2x 2 4x4x7 – + – x 3x 3 7x7x+ – 4x 24x 2 Multiply by x. x 2x 2 4x4x7 – + x 3x 3 15x+ – 2x 22x 2 +14 Combine like terms.

Example 5 Multiply Polynomials Horizontally Find the product. () 4+3x3x () 5x 25x 2 x6 – + a. 4+3x3x () 5x 25x 2 x6 – + () 5x 25x 2 x6 – + = Use distributive property. SOLUTION () 4+3x3x () 5x 25x 2 x6 – + a. + 15x 3 18x – +20x 2 4x4x24 – + = 3x 23x 2 Use distributive property. 15x 3 +24 – + = 20x 2 3x 23x 2 () + 18x4x4x – + () Group like terms. 15x 3 14x – + = 23x 2 24 – Combine like terms.

Homework: Worksheet 3.1 do ALL