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Math 105 Exam II Solution
2. Divide. (10)
(3x^{4}  5x^{3} + 4x^{2}  5x + 1)
(x^{2} + 1)
Solution :
We cannot use synthetic division since the divisor is not of the form xa. We
use long
division instead after rewriting the divisor as x^{2} + 0x + 1. We
obtain 3x^{2}  5x + 1.
3. Use the remainder theorem to find f(4), where f(x) = x^{4} x^{3}
 19x^{2} + 49x  30. (10)
Solution:
Use 4 for the synthetic division .
So f(4) = 54.
4. Solve the equation for p (10)
5. Simplify . (10)
Since the root is odd , we need no absolute values.
6. 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.
7. Factor completely .(10)
x^{2}(x + 3)  4(x + 3) = (x + 3)(x^{2}  4) = (x + 3)(x + 2)(x
 2)
8. Determine the domain of f. (10)
The domain of f 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 f is therefore {x ∈ R l x≠ 1, x ≠ 6}.
9. Divide and, if possible, simplify. (10)
Solution:
10. Find the LCD , then add and simplify. (10)
Solution:
11. Rosanna walks 2 mph slower than Simone. In the time it
takes Simone to walk 8 mi,
Rosanna walks 5 mi. Find the speed of each person. (10)
Solution:
d  r  t  
Rosanna  5  x  2  t 
Simone  8  x  t 
Since d = r . t, we have t
and .Setting the equations equal we get
Simone walks at a rate ofmph and Rosanna at a rate ofmph.
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