Answer:
C) 27.5
Step-by-step explanation:
C) 27.5
Answer:
1 4 2
Step-by-step explanation:
the polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r). In particular, x-r is a divisor (= a factor) of f(x), if and only if f(r)=0.
first we are dividing by x - 2.
so, r = 2.
as this is a factor, the remainder must be 0.
so,
0 = f(2) = 2³ + a2² - 15×2 + b = -22 + 4a + b
22 = 4a + b
then we divide by x + 3.
so, r = -3.
and the remainder is 75.
so,
75 = f(-3) = (-3)³ + a×(-3)² - 15×-3 + b = 18 + 9a + b
57 = 9a + b
now we have 2 equations with 2 variables to solve.
and since one term (+b) is the same in both equations, we use a little trick to subtract the first from the second equation.
57 = 9a + b
- 22 = 4a + b
---------------------
35 = 5a + 0
a = 7
22 = 4×7 + b = 28 + b
-6 = b
a = 7
b = -6
Part A)
A mixed number is in the form 
where W is any whole number part. The p and q are also whole numbers, which when combined together, form the fractional part p/q
To have a mixed number between 3 and 4, we must make the whole part W equal to 3. The p and q can be anything you want as long as p is smaller than q, this is so p/q is a fraction smaller than 1. So for example, we could have p = 2 and q = 7. So the mixed number 
is one example of a value between 3 and 4.
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Part B)
This seems to be asking the same exact thing as part A. I'll give another example. The mixed number 
is between 3 and 4. Again notice the whole part is W = 3. The other two pieces are p = 4 and q = 9. We have p smaller than q.
