Given that f(x)=3x^20 was translated to g(x)=3x^26. From the two expressions we see that the image has the same base as the pre-image. This implies that the image is very similar to the object. Hence the translation is a dilation. The scale factor will be:
image/object
=3x^26/3x^20
=3x^(26-20)
=3x^6
