1. Use the Rational Root theorem and long division to completely factor each of the following polynomials. a. f(x) = 4x^4 - 4x^3 - 4x^2 + 3x + 1 over the rationals. b. g(x) = x^3 - 2x^2 + 2x - 1 over the complex numbers. c. f(x) = x^3 + 7x + 48 over the complex numbers.
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According to the Rational Root Theorem, any rational root of this polynomial must be of the form ±p/q, where p is a factor of the constant term (1) and q is a factor of the leading coefficient (4). The possible rational roots are ±1, ±1/2, ±1/4. Now, we can test Show more…
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