Polynomial Division Techniques and Applications
Explore the use of Pascal's triangle, polynomial long division, and synthetic division for dividing polynomials in mathematics. Learn how to apply these methods, including evaluating polynomials and using the Remainder Theorem. Enhance your understanding of dividing polynomials by binomials and different techniques for polynomial division.
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Presentation Transcript
Bellwork Bellwork 1. Use Pascal s triangle to expand (? + 2?)4 2. Use Pascal s triangle to expand (? + 3)5
Dividing Polynomials Dividing Polynomials Section 4.3
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.
Bellwork ( ( ) ( ) + + 4 3 2 2 4 2 9 36 4 x x x x x ) ( ) 4 2 2 2 40 28 5 2 x x x x
Synthetic Division There is a shortcut for dividing polynomials by binomials of the form x k x k. This shortcut is called synthetic division. This method is shown in the next example.
Synthetic Division Divide Divide ??+ 4 + 4??+ 9 by (x + 9 by (x 3) 3)
Using Synthetic Division Using Synthetic Division Divide 3 Divide 3?? 2 2??+ 2 + 2? 5 by 5 by ? + 1. + 1.
Evaluating a Polynomial Use synthetic division to evaluate f(x) = 5?? ??+ 13? + 29 when ? = 4
