The presentation explains two methods for dividing polynomials, focusing on algebraic long division. It provides a step-by-step guide using the polynomial 2x^3 + 3x^2 - x + 1 divided by x + 2. The end result is a quotient of 2x^2 - x + 1 with a remainder of -1.

1. Dividing polynomials This PowerPoint presentation demonstrates two different methods of polynomial division. © Kristen A. Treglia 2007

2. Algebraic long division Divide 2 x ³ + 3 x ² - x + 1 by x + 2 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, 2 x ³, by x (the first term of the divisor). This gives 2x². This will be the first term of the quotient.

4. Algebraic long division Now multiply 2x² by x + 2 and subtract

5. Algebraic long division Bring down the next term, - x .

6. Algebraic long division Now divide – x ², the first term of – x ² - x , by x , the first term of the divisor which gives – x .

7. Algebraic long division Multiply –x by x + 2 To get a result of:

8. Algebraic long division Now subtract ** remember, you must subtract both the –x 2 term and the -2x term

9. Algebraic long division Now combine like terms (since we subtracted two negative terms they both turned into positive terms) {

10. Algebraic long division Bring down the next term, 1

11. Algebraic long division Divide x , the first term of x + 1, by x , the first term of the divisor which gives 1

12. Algebraic long division Multiply x + 2 by 1 and subtract

13. Algebraic long division The remainder is –1. The quotient is 2x² - x + 1