76. DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x) = 3x* – 5x' +x² – 3r + 5 Q(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* + 3x² – 2x² + 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?
76. DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x) = 3x* – 5x' +x² – 3r + 5 Q(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* + 3x² – 2x² + 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?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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DISCOVER: Nested Form of a Polynomial Expand Q to
prove that the polynomials P and Q are the same.
Transcribed Image Text:76. DISCOVER: Nested Form of a Polynomial Expand Q to
prove that the polynomials P and Q are the same.
P(x) = 3x* – 5x' +x² – 3r + 5
Q(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* + 3x² – 2x² + 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?
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