1. Factor completely .(10)
2. Determine the domain of f. (10)
The domain of g is the set of values x ∈ R for which the
denominator x ^2-7x+6 is not
equal to 0. To obtain the values that must be excluded from R, set the
denominator
equal to zero :
The domain of g is therefore
3. Divide and , if possible, simplify. (10)
Solution :
4. Find the LCD , then add and simplify . (10)
Solution :
5. Frank walks 2 km/h slower than Peter. In the time it
takes Peter to walk 8 km, Frank
walks 5 km. Find the speed of each person. (10)
Solution:
Since d = r * t, we have
and t=8/x. Setting the equations equal we
get
Peter walks at a rate of 16/3 km/h and Frank at a rate of
10/3 km/h.
6. Simplify. (10)
Solution:
7. Divide.
Solution:
We cannot use synthetic division since the divisor is not of the form x-a. We
use long
division instead after rewriting the divisor as x^2 + 0x + 1. We obtain 3x^2 -
5x + 1.
8. Use the remainder theorem to find h(4), where
. (10)
Solution:
Use 4 for the synthetic division .
So h(4) = 54.
9. Solve the equation 
for q. (10)
10. Simplify. (10)
Since the root is odd , we need no absolute values.
11. Divide and simplify . (10)
Since both x and y appear with odd powers under the
radical in the original expression, they both had to be positive in the first
place. Therefore, the final expression needs no absolute value.
