Understanding Polynomial Division Methods

Learn how to divide polynomials using long division and synthetic division techniques. Explore the processes of dividing polynomials by other polynomials or binomials, using the Remainder Theorem, and applying synthetic division to evaluate polynomials. Master the steps with detailed examples and visual aids.

• Polynomial division
• Synthetic division
• Long division
• Remainder Theorem
• Polynomial evaluation

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1. Dividing Polynomials Dividing Polynomials Section 4.3

2. Divide the polynomial

3. What You Will Learn Use long division to divide polynomials by other polynomials. Use synthetic division to divide polynomials by binomials of the form x k. Use the Remainder Theorem.

4. Using Polynomial Long Division

6. Synthetic Division There is a shortcut for dividing polynomials by binomials of the form x k. This shortcut is called synthetic division. This method is shown in the next example.

7. Synthetic Division Divide x3 + 4x2 + 9 by x 3

9. Using Synthetic Division Divide 3x3 2x2 + 2x 5 by x + 1.

12. Evaluating a Polynomial Use synthetic division to evaluate f(x) = 5x3 x2 + 13x + 29 when x = 4