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Adding and Subtracting Polynomials: Examples and Solutions

This resource covers the essential techniques for adding and subtracting polynomials through clear examples. We begin with basic principles, utilizing vertical and horizontal methods for adding polynomials. Key steps include aligning like terms and grouping them for straightforward computation. The process of subtraction is also illustrated, emphasizing the importance of combining like terms and using the distributive property for simplification. Practice problems are included to consolidate understanding. Perfect for students seeking to master polynomial operations.

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Adding and Subtracting Polynomials: Examples and Solutions

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  1. Adding and Subtracting Polynomials 1/6/2014

  2. Example 1 a. Add and – – – 2x3 4x2 x3 6x2 + + + x 9 5x 1 SOLUTION a. – 2x3 4x2 + + x 9 – – x3 6x2 + + 5x 1 – 3x3 2x2 + + 4x 8 Add Polynomials Vertically

  3. Example 1 – 5x2 2x 4x2 7x + + 3 – 3 5x2 4x2 2x 7x + + + = – 3 9x2 5x + = Add Polynomials Horizontally b. Add and Group like terms. Combine like terms.

  4. Example 2 SOLUTION Align like terms, then add the opposite of the subtracted polynomial. – – 6x3 x2 + 7x 12 – – – 3x3 4x2 + 9x – – – 3x3 5x2 2x 12 Subtract Polynomials (3

  5. Example 3 – – 8x2 4x 2x2 6x + 20 + + 14 Use distributive property. = – – 6x 20 14 + + + Group like terms. 8x2 2x2 4x = + + Combine like terms. 10x2 2x 6 = Use the Distributive Property Simplify the expression. a. ( ) ( ) – – 2x2 x x2 3x + + + 4 5 2 7

  6. Example 3 – – + – Group like terms. x4 x3 x3 x2 x2 x x 1 + + + = – Combine like terms. x4 2x 1 + = Use the Distributive Property Use distributive property. – – – x4 x3 x2 x x3 x2 x 1 + + + + =

  7. Homework: WS: Adding/Subtracting Polynomials

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