Practice COLLEGE ALGEBRA EXAM 1 Practice COLLEGE ALGEBRA EXAM 1

1. Simplify to an answer containing no negative exponents: [((4xy-1)3)/((2x-2y)2 )].


(4xy-1)3
(2x-2y)2
= 43 x3 (y-1)3
22(x-2)2y2
=
43 x3 y-1 ·3
4x-2 ·2y2
= 42 x3 y-3
x-4y2
= 42 x3x4
y3 y2
= 42 x7
y5
.




2. Extract squares: [(4(x + 1)2)]. Extract cubes: [3]8(x + 1)3.


  _______
4(x + 1)2
 
= 2|x+1|,
because nonnegativity is implicit in even radical symbol.
[3]8(x + 1)2 = 2(x+1), because odd roots are unique.




3. Solve: x2 = x4.


x4 - x2 = 0 x2(x+1)(x-1) = 0.
x = 0 or x = 1 or x = -1.




4. Find the domain of: [(x + 5 )] -[1/(x - 1)] .


No even rooting negative x+ 5 0.
No division by 0 x \not = 1.
-5 x < 1 or 1 < x.

5. A paints 1 room in 2 days. B paints 1 room in 5 days. If they work together, how many days does it take them to paint in 5 rooms?


(x days )

1 room
2 days
+ 1 room
5 days


= 5 rooms .
x = 5
1
2
+ 1
5
.




6. Reduce: [(4 - x2)/(x2 - 4x + 4)] .


4 - x2
x2 - 4x + 4
= (2-x)(2+x)
(x-2)(x-2)
= - x +2
x-2
.




7. Factor into irreducible factors: 7(x2 - 2x + 1) - 3(x-1).


7(x2 - 2x + 1) - 3(x-1) = 7(x-1)(x-1) - 3(x-1) =
(7(x-1) - 3)(x-1) = (7x - 10)(x-1).




8. Find the quotient and remainder (x4 + 2) (3x3 - 1).


x4
3x3
= 1
3
x.
(x4 + 2)- ( 1
3
x (3x3 - 1)) = 1
3
x + 2 = Remainder.
Quotient = 1
3
x .




9. Write the product (x-2)2(x+2)2 as a polynomial in standard form.


(x-2)2(x+2)2 = (x-2)(x+2)(x-2)(x+2) =
(x2 - 4) (x2 - 4) = x4 - 8x2 + 16.




10. Solve for the exact answer: 3(x + 2) + 1 = 2 x - 2.


Isolate: 3 x - 2x = - 2 3 - 2 -1.
Factor: (3 - 2)x = - 2 3 - 2 -1 .
x = - 2 3 - 2 -1
3 - 2
.




File translated from TEX by TTH, version 2.80.
On 28 Jan 2001, 15:23.