What of the following is the complete factorization of the polynomial - x^3+2x^2+x+2 A.(x+2)(x+i)(x-i)
B. (x-2)(x+i)(x-i)
C. (x-2)(x+i)(x+i)
D. (x+2)(x+i)(x+i)

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  A. (x +2)(x +i)(x -i)

Step-by-step explanation:

The complex factors must be conjugates, eliminating choices C and D.

The product of the complex factors will be (x^2 +1) so the remaining factor must have a constant of +2 in order for the constant in the product to be 2.

  p(x) = (x +2)(x² +1) = (x +2)(x +i)(x -i)

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