Download MTH 209 Final Examination

MTH 209
Name
1. Use the distributive property to find the product of (and then combine terms for):
(y2z – 4y4)(y2z + 3z2 - y4)
Multiply out:
y^4z^2 + 3y^2z^3 – y^6z – 4y^6z – 12y^4z^2 + 4y^8
Combine like terms:
-11y^4z^2 + 3y^2z^3 – 5y^6z + 4y^8
Perform the indicated operations:
2. (k – 4)(k + 9) – (k – 3)(k + 7)
FOIL:
k^2 + 5k – 36 – (k^2 + 4k – 21)
k^2 + 5k – 36 – k^2 – 4k + 21
k - 15
3.
10x2y4 + 4x4y2 – 16x6y3
-2x2y2
Divide each term:
10x^2y^4/(-2x^2y^2) + 4x^4y^2/(-2x^2y^2) – 16x^6y^3/(-2x^2y^2)
Do the division:
-5y^2 – 2x^2 + 8x^4y
4.
3x 4  11x9
3*11 = 33
x^4 * x^9 = x^(4+9) = x^13
33x^13
Simplify and express without negative exponent
22 w4
5.
2 w2
-22/2 = -11
w^-4 / w^-2 = w^2/w^4 = 1/w^2
answer:
-11/w^2
Perform computation with scientific notation:
6. (3.5 x 1035)(2.2 x 1010)
4.4 x 1015
3.5*2.2/4.4 = 1.75
10^35 * 10^10 / 10^15 = 10^(35+10-15) = 10^30
Answer:
1.75 * 10^30
7. Factor out the GCF in 56x3y5 + 64x4y3 – 16x5y4
Factor out 8x^3y^3:
8x^3y^3 ( 7y^2 + 8x – 2x^2y )
8. Factor completely: x3y + 2x2y2 + xy3
Factor out xy:
xy(x^2 + 2xy + y^2)
Factor the inside as a square:
xy(x+y)^2
9. Factor completely: 3h2t + 6ht + 9t
Pull out 3t:
3t(h^2 + 2h + 3)
The inside cannot be factored.
10. Factor completely: 3x2 – 17x + 10
(3x+a)(x+b)
ab = 10
a+3b = -17
a = -2, b = -5
(3x-2)(x-5)
11. x cannot have what values in this rational expression:
set the bottom to 0:
x^2 + 4x – 21 = 0
factor:
(x+7)(x-3) = 0
X cannot be -7 or 3
12. Perform indicated operations: 22 x 2 y 3 z 
7 x5
55 y 3 z 4
22*7/55 = 14/5
x^2y^3zx^5 / y^3z^4 = x^7/ z^3
answer:
14x^7
------5z^3
13. Perform indicated operations:
w  2 4w  8

(division)
3w
6w
Flip the second and multiply and factor:
(w-2)(6w)
-----------3w(4)(w-2)
Cancel the w and w-2:
6 / (3*4)
= 1/2
3x  6
x  4 x  21
2
14. Perform indicated operations:
x
3x
 2
x  2x  3 x  9
2
Get a common denominator:
(x-3)(x+3)(x+1)
x(x+3)/ CD - 3x(x+1) / CD
(x^2 + 3x – 3x^2 – 3x) / CD
-2x^2 / CD
Answer:
-2x^2 / ((x-3)(x+3)(x+1))
15. Find the product of ( 5  9)( 5  9)
Difference of squares:
5 – 81
= -76
16. Solve
5 3x  1

8 2 x  10
Cross multiply:
5(2x+10) = 8(3x+1)
10x + 50 = 24x + 8
42 = 14x
X=3
17. Find all real solutions for (a – 4)2 = 36
Square root:
a-4 = +/- 6
Add 4:
a = 4 +/- 6
a = 10 or -2
1 1

x y
18. Simplify:
5 5

x y
Get a common denominator:
(y/xy + x/xy) / (5y/xy + 5x/xy)
Combine terms:
(y+x)/xy / (5y+5x)/xy
Simplify:
(y+x)/(5y+5x)
= 1/5
19. Solve and check for extraneous solutions: x  2  x2  6
Square:
x^2 + 4x + 4 = x^2 + 6
Simplify:
4x – 2 = 0
4x = 2
X = 1/2
Check: ½+2 = 5/2, sqrt(1/4+6) = 5/2, YES
20, Solve using any method: x2 +14x + 49 = 0
Factor:
(x+7)^2
X = -7
21. Solve by any method: x2 + 6x -10 = 0
quadratic:
x = (-6 +/- sqrt(6^2-4*1*-10))/2
x = (-6 +/- sqrt(76))/2
x = -3 +/- sqrt(19)
x = -3+sqrt(19) or -3-sqrt(19)
22. The sum of the squares of two consecutive odd integers is 202. Find the integers.
x^2 + (x+2)^2 = 202
x^2 + x^2 + 4x + 4 = 202
2x^2 + 4x – 198 = 0
x^2 + 2x – 99 = 0
(x-9)(x+11) = 0
X = 9 or -11
Can’t be negative, so x = 9, x+2 = 11.
The numbers are 9 and 11.
23. The length of Joe’s office is 3 feet longer than its width. The diagonal of his office
measures 15 feet. What are the length and width of Joe’s office?
x^2 + (x+3)^2 = 15^2
x^2 + x^2 + 6x + 9 = 225
2x^2 + 6x – 216 = 0
x^2 + 3x – 108 = 0
(x+12)(x-9) = 0
X = -12 or 9
Can’t be negative, so it is 9 and 12 feet.
24. If 340 of 560 voters surveyed said that they would vote for the incumbent, then how
many votes could the incumbent expect out of 843,000 votes?
340/560 = x/843000
Cross multiply:
560x = 340*843000
X = 340*843000/560
X = about 511821
25. If air resistance is neglected, the number that of feet, s, that an object falls during t
seconds is given by the equation s = 16t2. How long would it take it for an engine of
an airplane to reach the earth if it fell off the airplane at 24,000 feet?
24000 = 16t^2
t^2 = 1500
Square root (the positive one):
T = 38.73 seconds