dividing-polynomials-slide-share-1196832292862534-5-converted.pptx
- 1. Dividing polynomials This PowerPoint presentation demonstrates two different methods of polynomial division. © Kristen A. Treglia 2007
- 2. Algebraic long division Divide 2x³ + 3x² - x + 1 by x + 2 x 2 2x 3 3x 2 x 1 x + 2 is the divisor The quotient will be here. 2x³ + 3x² - x + 1 is the dividend
- 3. Algebraic long division First divide the first term of the dividend, 2x³, by x (the first term of the divisor). 2x 2 x 2 2x 3 3x 2 x 1 This gives 2x². This will be the first term of the quotient.
- 4. Algebraic long division x 2 2x 3 3x 2 x 1 2x 3 4x 2 2x 2 x 2 Now multiply 2x² by x + 2 and subtract
- 5. Algebraic long division Bring down the next term, -x. 2x 3 4x 2 2x 2 x 2 2x 3 3x 2 x 1 x 2 x
- 6. Algebraic long division 2x 3 4x 2 x 2 x 2x 2 x x 2 2x 3 3x 2 x 1 Now divide –x², the first term of –x² - x, by x, the first term of the divisor which gives –x.
- 7. Algebraic long division x 2 x 2x 2 x x 2 2x 3 3x 2 x 1 2x 3 4x 2 x 2 2x x Multiply –x by x + 2 and subtract
- 8. Algebraic long division Bring down the next term, 1 x 2 x 2x 2 x x 2 2x 3 3x 2 x 1 2x 3 4x 2 x 2 2x x 1
- 9. Algebraic long division Divide x, the first x 2 2x 3 3x 2 x 1 2x 3 4x 2 x 2 x 2x 2 x 1 x 2 2x x 1 term of x + 1, by x, the first term of the divisor which gives 1
- 10. Algebraic long division x 2 x x 2 2x 2x 2 x 1 x 2 2x 3 3x 2 x 1 2x 3 4x 2 x 1 x 2 1 Multiply x + 2 by 1 and subtract
- 11. Algebraic long division The remainder is –1. x 2 2x 3 3x 2 x 1 2x 3 4x 2 x 2 x x 2 2x 2x 2 x 1 x 1 x 2 1 The quotient is 2x² - x + 1