Question

Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = x^4 + 6x^3 + 12x^2 + 24x + 32 A. f(x) = (x - i?8) (x + i?8) (x - 2)(x + 2) B. f(x) = (x - 1)(x - 8)(x - 2 i)(x + 2 i) C. f(x) = (x - 2)(x + 4)(x - 2)(x + 2) D. f(x) = (x + 2)(x + 4)(x - 2 i)(x + 2 i)

          Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = x^4 + 6x^3 + 12x^2 + 24x + 32
A. f(x) = (x - i?8) (x + i?8) (x - 2)(x + 2)
B. f(x) = (x - 1)(x - 8)(x - 2 i)(x + 2 i)
C. f(x) = (x - 2)(x + 4)(x - 2)(x + 2)
D. f(x) = (x + 2)(x + 4)(x - 2 i)(x + 2 i)

Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = x^4 + 6x^3 + 12x^2 + 24x + 32
A. f(x) = (x - i?8) (x + i?8) (x - 2)(x + 2)
B. f(x) = (x - 1)(x - 8)(x - 2 i)(x + 2 i)
C. f(x) = (x - 2)(x + 4)(x - 2)(x + 2)
D. f(x) = (x + 2)(x + 4)(x - 2 i)(x + 2 i)

Added by Phillip A.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Allison Knapp

08/09/2023

Step 1

The Rational Root Theorem states that any rational zero of a polynomial with integer coefficients must be of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is 32 and the Show more…

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Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = x^4 + 6x^3 + 12x^2 + 24x + 32 A. f(x) = (x - i√8)(x + i√8)(x - 2)(x + 2) B. f(x) = (x - 1)(x - 8)(x - 2i)(x + 2i) C. f(x) = (x - 2)(x + 4)(x - 2)(x + 2) D. f(x) = (x + 2)(x + 4)(x - 2i)(x + 2i)