SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x^4 + 4x^3 + 13x^2 + 16x + 4 a. f(x) = (3x - 1)(x - 1)(x + 2)(x

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Question 1061307: Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3x^4 + 4x^3 + 13x^2 + 16x + 4
a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)

Found 2 solutions by KMST, ikleyn:
Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
The polynomial function is obviously positive for all positive values of x,
so there are no positive zeros, and no factors such as (x-1) or (x-2),
so the only reasonable choice is c.

Answer by ikleyn(52787) (Show Source):
You can put this solution on YOUR website!
.
Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3x^4 + 4x^3 + 13x^2 + 16x + 4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Case b), of course.

Plot y =

You can easily check it by making direct calculations.

SOLUTION: Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x^4 + 4x^3 + 13x^2 + 16x + 4 a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2) b.