after solving this question post it as an image If a polynomial p(x) can be factored as a product of two lower degreepolynomials p₁ (x) and p₂(x) asp(x) = P₁(x)p2(x)then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary squarematrix A. Verify this statement for polynomialsp(x)=x²-9,P₁(x) = x+3, p2(x) = x - 3.

If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as p(x) = p₁(x)p₂(x) then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x) = x² − 9, P₁(x)=x+3, p₂(x) = x − 3.

If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as p(x) = p₁(x)p₂(x) then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x) = x² − 9, P₁(x)=x+3, p₂(x) = x − 3.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.CT: Chapter Test

Problem 9CT

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Question

after solving this question post it as an image

If a polynomial p(x) can be factored as a product of two lower degree
polynomials p₁ (x) and p₂(x) as
p(x) = P₁(x)p2(x)
then it can be proved that p(A) = P₁(A)p2(A) for an arbitrary square
matrix A. Verify this statement for polynomials
p(x)=x²-9,
P₁(x) = x+3, p2(x) = x - 3.

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