A polynomial P is given.P(x) = x5 − 625x(a) Factor P into linear and irreducible quadratic factors with real coefficients.
Question
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.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv
Similar Questions
A polynomial P is given.P(x) = x5 − 625x(a) Factor P into linear and irreducible quadratic factors with real coefficients.
P(x)=x4−3x3+kx2−6x+14𝑃(𝑥)=𝑥4−3𝑥3+𝑘𝑥2−6𝑥+14, where k is an unknown real number.If (x−2)(𝑥−2) is a factor of this polynomial, what is the value of k?
The characteristic quadratic polynomial of homogeneous second-order recurrence relation with constant coefficients recurrence relation is
Given x − 6 is a factor of f(x) = x3 + 5x2 − 48x − 108, determine the othertwo linear factors of f(x).
Let p be a prime number. The quadratic equation having its roots as factors of p is(a) x2 –px +p=0 (b) x2–(p+1)x +p=0 (c) x2+(p+1)x +p=0 (d) x2 –px+p+1=0