Remainder Theorem says that if there is any Polynomial equation P(x), which is to be divided by (x - a) then remainder can be calculated by substituting value of a in equation P(x).
= P(x) divided by
Step 1: Find a
To find a we will have to convert (x+2) into (x - a) form
i.e. (x+2) = (x - (-2))
therefore, a = -2
Step 2: Substitute value of a in P(x),
By substitution we get,
=
=
= = Remainder
Hence, Remainder is 55.
Answer:
Option C.
The distance from the point to the circle is 6 units
Step-by-step explanation:
we know that
The distance between the circle and the point will be the difference of the distance of the point from the center of circle and the radius of the circle
step 1
Find the center and radius of the circle
we have
Convert to radius center form
Complete the square
Rewrite as perfect squares
so
The center is the point (0,4)
The radius is
step 2
Find the distance of the point from the center of circle
the formula to calculate the distance between two points is equal to
we have
(6,-4) and (0,4)
substitute the values
step 3
Find the difference of the distance of the point from the center of circle and the radius of the circle
therefore
The distance from the point to the circle is 6 units
see the attached figure to better understand the problem
