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)322(x-2)2y2 =
 43 x3 y-1 ·34x-2 ·2y2 = 42 x3 y-3x-4y2 = 42 x3x4y3 y2 = 42 x7y5 .

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

 _______Ö4(x + 1)2 = 2|x+1|,
 because nonnegativity is implicit in even radical symbol.
 Ö[3]8(x + 1)2 = 2(x+1), because odd roots are unique.

3. Solve: x2 = x4.

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

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

 No even rooting negative Þ x+ 5 ³ 0.
 No division by 0 Þ 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 ) æç è 1 room 2 days + 1 room 5 days ö÷ ø = 5 rooms .
x = 5
 12 + 15
.

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

 4 - x2x2 - 4x + 4 = (2-x)(2+x)(x-2)(x-2) = - x +2x-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).

 x43x3 = 13 x.
 (x4 + 2)- ( 13 x (3x3 - 1)) = 13 x + 2 = Remainder.
 Quotient = 13 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: Ö3(x + 2) + 1 = 2 x - Ö2.

 Isolate: Ö3 x - 2x = - 2 Ö3 - Ö2 -1.
 Factor: (Ö3 - 2)x = - 2 Ö3 - Ö2 -1 .
 x = - 2 Ö3 - Ö2 -1Ö3 - 2 .

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On 28 Jan 2001, 15:23.