DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x) = 3x* - 5x³ + x² – 3x + 5 O(x) = (3x – 5)x + 1)x – 3)x + 5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x) = x - 2x + 3x – 2x + 3x + 4 in "nested" form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a poly- nomial using synthetic division?
DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x) = 3x* - 5x³ + x² – 3x + 5 O(x) = (3x – 5)x + 1)x – 3)x + 5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x) = x - 2x + 3x – 2x + 3x + 4 in "nested" form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a poly- nomial using synthetic division?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.3: Dividing Polynomials
Problem 76E
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