In the diagram, JM PR, MK RQ, and KJ QP. LA
M
R
K
Q
Select and drag tiles to the empty boxes to correctly complete each sentence.
Using transformations, such as a'
it can be verified that AJKM is congruent to APQR
if all pairs of corresponding angles are congruent.
In any pair of triangles, if it is known that all pairs of corresponding sides are congruent, then the triangles
congruent.

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.