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Understanding Polynomial Long Division: Step-by-Step Guide

Dive into the process of dividing polynomials using long division, a method similar to integer long division. Follow clear, step-by-step examples illustrating how to divide polynomials, including handling missing terms. Explore various scenarios, from simple polynomial division to testing if one polynomial is a factor of another. This comprehensive guide provides the knowledge and tools necessary for mastering polynomial long division, ensuring you can tackle even complex expressions confidently.

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Understanding Polynomial Long Division: Step-by-Step Guide

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  1. Lesson 38 Dividing polynomials using long division

  2. division • Polynomial long division is a similar process to integer long division. quotient dividend divisor

  3. divide • (12x3 - 6x2 + 5x + 4) by 3x • 4x2 -2x + 1 • 3x 12x3 - 6x2 + 5x + 4 • subtract12x3 • 0 - 6x2 +5x + 4 • subtract- 6x2 • 0 + 5x + 4 • subtract3x • 2x + 4 • answer 4x2 - 2x + 1 + 2x+4 • 3x

  4. divide • (32x4 - 104x3 + 56x2 + 11x + 4) by 8x

  5. Dividing a polynomial by a polynomial • Divide: • (x4 + 2x3 - 13x2 - 38x -24) by ( x+4) • (3x4 + 11x3 - 55x2 + 113x + 79) by (x +7)

  6. Dividing a polynomial by a polynomial with missing terms • Divide: • (4x4 - x3 - 11x - 484) by (x2 + 11) • Even though there are missing terms, include a place for them and divide as usual. • (4x4 -x3 + 0x2 -11x -484) by(x2 + 0x + 11) • (4x4 + 8x3 -55x2 + 24x) by (x2 + 3)

  7. Testing if one polynomial is a factor of another • Is (x+2) a factor of 2x3 -x2 -7x +6 • Divide - if remainder is 0, then it is a factor. • Is (x+3) a factor of 6x3 -6x2 -6x + 6? • Is (x+5) a factor of 8x3 +37x2 -11x + 20? • Is (x+6) a factor of 4x3 +35x2 +73x +150?

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