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Adding and Subtracting Polynomials: Examples and Guided Practice

Learn how to add and subtract polynomials vertically and horizontally through examples and guided practice. Includes step-by-step solutions.

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Adding and Subtracting Polynomials: Examples and Guided Practice

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  1. a.2x3 – 5x2 + 3x – 9 + x3 + 6x2 + 11 3x3 + x2 + 3x + 2 EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2x3 – 5x2 + 3x – 9 andx3 + 6x2 + 11 in a vertical format. SOLUTION

  2. EXAMPLE 1 Add polynomials vertically and horizontally b. Add 3y3 – 2y2 – 7y and – 4y2 + 2y – 5 in a horizontal format. (3y3 – 2y2 – 7y) + (– 4y2 + 2y – 5) = 3y3 – 2y2 – 4y2 – 7y + 2y – 5 = 3y3 – 6y2 – 5y – 5

  3. 8x3 – x2 – 5x + 1 8x3 – x2 – 5x + 1 – (3x3 + 2x2–x + 7) + – 3x3– 2x2 + x – 7 5x3 – 3x2 – 4x – 6 EXAMPLE 2 Subtract polynomials vertically and horizontally a. Subtract 3x3 + 2x2 – x + 7 from 8x3 – x2 – 5x + 1 in a vertical format. SOLUTION a. Align like terms, then add the opposite of the subtracted polynomial.

  4. EXAMPLE 2 Subtract polynomials vertically and horizontally b. Subtract 5z2 – z + 3 from 4z2 + 9z – 12 in a horizontal format. Write the opposite of the subtracted polynomial, then add like terms. (4z2 + 9z – 12) – (5z2–z + 3) = 4z2 + 9z – 12 – 5z2 + z – 3 = 4z2 – 5z2 + 9z + z – 12 – 3 = – z2 + 10z – 15

  5. t2 – 6t + 2 + 5t2 – t – 8 for Examples 1 and 2 GUIDED PRACTICE Find the sum or difference. 1. (t2 – 6t + 2) + (5t2 – t – 8) SOLUTION 6t2 – 7t – 6

  6. for Examples 1 and 2 GUIDED PRACTICE 2. (8d – 3 + 9d3) – (d3 – 13d2 – 4) SOLUTION = (8d – 3 + 9d3) – (d3 – 13d2 – 4) = (8d – 3 + 9d3) – d3 + 13d2 + 4) = 9d3 –3 d3 + 13d2 + 8d – 3 + 4 = 8d3 + 13d2 + 8d + 1

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