sat-dog

Choice B is correct. The given expression can be factored by first finding two values whose sum is $20$ and whose product is $3\left(-63\right)$, or $-189$. Those two values are $27$ and $-7$. It follows that the given expression can be rewritten as $3x^2+27x-7x-63$. Since the first two terms of this expression have a common factor of $3x$ and the last two terms of this expression have a common factor of $-7$, this expression can be rewritten as $3x\left(x+9\right)-7\left(x+9\right)$. Since the two terms of this expression have a common factor of $\left(x+9\right)$, it can be rewritten as $\left(3x-7\right)\left(x+9\right)$. Therefore, expression II, $3x-7$, is a factor of $3x^2+20x-63$, but expression I, $x-9$, is not a factor of $3x^2+20x-63$. 

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.