For the polynomial x^4 – 4: • find all roots and graph them in the complex plane. factor the polynomial completely over the rational numbers. factor the polynomial completely over the real numbers. • factor the polynomial completely over the complex numbers. (b) do the same for the polynomial x4 + 4. (c) what are the principal fourth roots of 4 and of -4? explain.

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the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct