Answer:
See below.
Step-by-step explanation:
Triangle ABC will be right-angled if 2 of its sides are perpendicular to each other. When sides are perpendicular the product of their slopes = -1.
Slope of side AB = (-3-2)/(2-5) = -5/-3 = 5/3
Slope of side BC = (3- -3) / -8-2) = 6/-10 = -3/5
The product of the slopes = 5/3 * -3/5 = -15/15 = -1.
So AB is perpendicular to BC and triangle ABC is right-angled .
The method we need to use here is very particular to this type of a situation. The way we will find that polynomial, or the divisor, is to follow this formula:

. For us that will look like this:

. First we will simplify as much as possible that very long numerator there. It simplifies to

. What you do now is use long division of polynomials, which, unfortunately, is impossible to show in this forum. However, get familiar with the long division process if you are not already, and you will find that your polynomial g(x) is

.
Answer:
1/169
Step-by-step explanation:
There are 4 aces in a deck of 52.
The probability that the first card is an ace is 4/52.
Since the card is replaced, the probability that the second card is an ace is also 4/52.
The total probability is (4/52) (4/52) = 1/169.