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Math 105 Exam II

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)

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)

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)

7. Divide.

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)

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.

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