1. Factor completely .(10)

2. De termine 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 s lower 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 ex pression , they both had to be positive in the first
place. Therefore, the final expression needs no absolute value.