MTH315Tutorial Activity 14Factorization of Polynomials over a FieldDetermine whether or not the polynomial 2x+3x² -7x-5 is an irreducible polynomial inZ₁₁ [x]. If the polynomial is reducible, then factor it into a product of irreduciblepolynomials.

Answered: Image /qna-images/answer/4bc03fa9-8196-4f6e-b561-9db8eabc08bc.jpg

Answered: Determine whether or not the polynomial…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 6TFE

See similar textbooks

Similar questions

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?
1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic polynomial of least degree with real coefficients that has the given numbers as zeros. a. b. c. d. e. f. g. and h. and
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. 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.
Finding a Polynomial with Specified Zeros Find a polynomial with integer coefficients that satisfies the given conditions. S has degree 4 and zeros 2i and 3i .
Prove the Unique Factorization Theorem in (Theorem). Theorem Unique Factorisation Theorem Every polynomial of positive degree over the field can be expressed as a product of its leading coefficient and a finite number of monic irreducible polynomials over . This factorization is unique except for the order of the factors.
Finding a Polynomial with Specified Zeros Find a polynomial with integer coefficients that satisfies the given conditions. T has degree 4, zeros i and 1+i , and constant term 12.
True or False Label each of the following statement as either true or false. 11. Every primitive polynomial is monic.

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Determine whether or not the polynomial 2x³ +3x²-7x-5 is an irreducible polynomial in Z₁₁ [x]. If the polynomial is reducible, then factor it into a product of irreducible polynomials.