A polynomial P is given.P(x) = x5 − 625x(a) Factor P into linear and irreducible quadratic factors with real coefficients.

Question

A polynomial P is given.P(x) = x5 − 625x(a) Factor P into linear and irreducible quadratic factors with real coefficients.
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Solution 1

The given polynomial is P(x) = x^5 - 625x.

First, we can factor out an x from each term to simplify the polynomial:

P(x) = x(x^4 - 625).

Next, we recognize that x^4 - 625 is a difference of squares, which can be factored as follows:

x^4 - 625 = (x^2 - 25)(x^2 + 25).

Again, we see that x^2 - 25 Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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