What is the completely factored form of this polynomial (selected answer is wrong)

Option D.

Step-by-step explanation:

A straightforward way to solve this type of problems is to expand all the options and see which one fits the desired one.

First let's see which options we can discard.

The original polynomial is:

p(x) = 2*x^5 + 12*x^3 - 54*x

So the degree of this polynomial is 5.

We can see that in option B we have only 3 "x", then the degree of this polynomial will be 3, then this option can be discarded.

Now let's try with the other 3 options:

A) = 2*x*(x^2 - 3)*(x + 9)*(x - 9)

    = 2*x*(x^2 -  3)*(x^2 - 81)

    = (2*x^3 - 6*x)*(x^2 - 81)

    = 2*x^5 - (2*x^3)*81 - 6*x^3 + 6*x*81

    = 2*x^5  -168*x^3 + 486*x

We can see that the second and third coefficients are different than the ones we wanted, so this is not the correct option.

Now let's try option D.

D) = 2*x*(x^2 - 3)*(x^2 + 9)

    = 2*x*(x^4 - 3*x^2 + 9*x^2 - 27) = 2*x*(x^4 + 6*x^2 - 27)

    = 2*x^5 + 2*6*x^3 - (27)*2x

    = 2*x^5 + 12*x^3 - 54*x

This is exactly what we wanted, so we can conclude that the correct option is D.

16

step-by-step explanation: