Practice COLLEGE ALGEBRA EXAM 1
Practice COLLEGE ALGEBRA EXAM 1
1. Simplify to an answer containing no negative exponents:
[((4xy^{1})^{3})/((2x^{2}y)^{2} )].

(4xy^{1})^{3} (2x^{2}y)^{2}

= 
4^{3} x^{3} (y^{1})^{3} 2^{2}(x^{2})^{2}y^{2}

= 
 
4^{3} x^{3} y^{1 ·3} 4x^{2 ·2}y^{2}

= 
4^{2} x^{3} y^{3} x^{4}y^{2}

= 
4^{2} x^{3}x^{4} y^{3} y^{2}

= 
4^{2} x^{7} y^{5}

. 


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

 _______ Ö4(x + 1)^{2}

= 2x+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: x^{2} = x^{4}.
x^{4}  x^{2} = 0 Þ x^{2}(x+1)(x1) = 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. 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 ) 
æ ç
è


1 room 2 days

+ 
1 room 5 days

ö ÷
ø

= 5 rooms . 
 

6. Reduce: [(4  x^{2})/(x^{2}  4x + 4)] .

4  x^{2} x^{2}  4x + 4

= 
(2x)(2+x) (x2)(x2)

=  
x +2 x2

. 


7. Factor into irreducible factors: 7(x^{2}  2x + 1)  3(x1).
7(x^{2}  2x + 1)  3(x1) = 7(x1)(x1)  3(x1) = 
 (7(x1)  3)(x1) = (7x  10)(x1). 


8. Find the quotient and remainder (x^{4} + 2) ¸(3x^{3}  1).

(x^{4} + 2) ( 
1 3

x (3x^{3}  1)) = 
1 3

x + 2 = Remainder. 
 

9. Write the product (x2)^{2}(x+2)^{2} as a polynomial in standard form.
(x2)^{2}(x+2)^{2} = (x2)(x+2)(x2)(x+2) = 
 (x^{2}  4) (x^{2}  4) = x^{4}  8x^{2} + 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 1 Ö3  2

. 


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On 28 Jan 2001, 15:23.