#20 Find the characteristic polynomial of A. Use x for the variable in your polynomial. You do not need to factor yourpolynomial.20-315 -3 -90 0 -1characteristic polynomial of A is: 0A

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Answered: Find the characteristic polynomial of…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.8: Factoring Pattern For X2+bx+c, C Negative

Problem 36WE

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DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)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)=x52x4+3x32x2+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 polynomial using synthetic division?
a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant polynomial in Z3[ x ], if one exists, that is a unit. c. Prove or disprove that there exist nonconstant polynomials in Zp[ x ] that are units if p is prime.
11. a. List all the polynomials in that have degree 2. b. Determine which of the polynomials in part a are units. If none exists, state so.
(a) If a is a zero of polynomial P. then _________mustbe a factor of P(x). (b) If a is a zero of multiplicity m of the polynomial P, then _______must a factor Of P(x) when we factor P completely.
The polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________

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Find the characteristic polynomial of A. Use x for the variable in your polynomial. You do not need to factor your polynomial. 20-3 A 15 -3 -9 0 0 -1 characteristic polynomial of A is: 0