Find the characteristic polynomial of A. Use x for the variable in your polynomial. You do not need to factor your polynomial.3 24 -6A = 0 -3 10 -12 4characteristic polynomial of A is: 0

formula for characteristic polynomial is A-xIwhere I is identity matrix I=100010001xI=x000x000x

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 35WE

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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?
The polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________
(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.
(a) Give the general form of polynomial function P of degree n. (b) What does it mean to say that c is a zero of P? Give two equivalent conditions that tell us that c is a zero of P.
If we divide the polynomial P by the factor xc and we obtain the equation P(x)=(xc)Q(x)+R(x), then we say that xc is the divisor, Q(x) is the _________, and R(x) is the ________.
a If we divide the polynomial P(x) by the factor xc and we obtain a remainder of 0, then we know that c is a ________ of P. b If we divide the polynomial P(x) by the factor xc and we obtain a remainder of k, then we know that P(c)=.

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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 polynomia 3 24 -6 A 0 -3 1 0 -12 4 characteristic polynomial of A is: 0