A+ Answers
Thehonest
1.docFactor COMPLETELY when possible. If the polynomial is prime, say so.
1. X2 – 3XY – 54Y2
2. 81a2 + 4b2
3. 10M4 – 25M2 + 20MN
4. 28X3 + 8X2 + 49X + 14
5. 8X2 + 17X – 21
6. 10Y2 + 11Y – 6
7. 6T2 + 5ST – 6S2
8. 64X3 – 27Y3
Solve each equation for the given variable.
9. y(5y + 13) = 6
10. 4T2 – 32T + 60 = 0
11. X3 + 6X2 – X – 6 = 0
12. 4X(X + 2) = (3X – 3)(X + 2)
Solve the following problems.
13. The length of a rectangular storage room floor is 5 feet longer than its width. If the area of the floor is 66 square feet, find its dimensions.
14. If h = -16t2 + 192t represents the height of a firework, in feet, t seconds after it was fired, when will the firework be 576 feet high?
15. A manufacturer determines that the profit in dollars for manufacturing n units is
P = 2n2 – 70n + 20. Assume n is a positive integer. How many units must be
produced to create a profit of $420?
16.
Find the domain of
f x( ) = 7x − 5 3x2 −13x −10
fx
()
=
7x-5
3x
2
-13x-10
Simplify each rational expression:
17.
x2 − 3xy −10y2
x2 + 7xy +10y2
x
2
-3xy-10y
2
x
2
+7xy+10y
2
18.
16X2 − 9 15X2 + 25X
* 30X3 −15X2
8X2 + 2X − 2
16X
2
-9
15X
2
+25X
*
30X
3
-15X
2
8X
2
+2X-2
19.
X2 + X − 6 X2 − 2X −15
÷ X2 + 2X − 8 X2 − X − 20
X
2
+X-6
X
2
-2X-15
¸
X
2
+2X-8
X
2
-X-20
20.
8x2 −10x − 3 −2x2 − 8x
* x2 + x 16x2 −1
⎛ ⎝⎜
⎞ ⎠⎟ ÷
−10x −15 8x5
⎛ ⎝⎜
⎞ ⎠⎟
8x
2
-10x-3
-2x
2
-8x
*
x
2
+x
16x
2
-1
æ
è
ç
ö
ø
÷
¸
-10x-15
8x
5
æ
è
ç
ö
ø
÷
Add or subtract:
21.
Y + 5 Y − 4
− Y + 3 Y + 7
Y+5
Y-4
-
Y+3
Y+7
22.
X − 2 X2 − X − 2
− 4
X2 −1 +
4X + 2 X2 − 3X + 2
X-2
X
2
-X-2
-
4
X
2
-1
+
4X+2
X
2
-3X+2
23.
25x2 − 4 5x3y7
5x + 2( ) 25x4y9
25x
2
-4
5x
3
y
7
5x+2
()
25x
4
y
9
24.
7 2X2
− 5X 6X3
⎛ ⎝⎜
⎞ ⎠⎟
3X 2
+ 7 3X2
⎛ ⎝⎜
⎞ ⎠⎟
7
2X
2
-
5X
6X
3
æ
è
ç
ö
ø
÷
3X
2
+
7
3X
2
æ
è
ç
ö
ø
÷
Solve each rational equation
25.
2T − 5 T + 3
= 2T + 9 T − 7
2T-5
T+3
=
2T+9
T-7
26.
Y − 4 Y +1
+ Y +1 Y − 4
= 13Y
Y 2 − 3Y − 4
Y-4
Y+1
+
Y+1
Y-4
=
13Y
Y
2
-3Y-4
27.
x − 2 x2 − 2x − 2
+ x + 5 x2 −1
= 4x + 3
x2 − 4x + 3
x-2
x
2
-2x-2
+
x+5
x
2
-1
=
4x+3
x
2
-4x+3
Simplify the expression
28.
72a5bc12
72a
5
bc
12
29.
7 3x2 − 5y − 4 5y + 9 7x2
73x
2
-5y-45y+97x
2
30.
4y3 8y4 − 7 y3( )
4y
3
8y
4
-7y
3
()
31.
7 x − 2 y( ) 7 x + y( )
7x-2y
()
7x+y
()
Rationalize the denominator in each expression below
32.
8 5 7b
8
57b
33.
7 3 + 5
7
3+5
34.
2 y − 7 3 y + 2
2y-7
3y+2
35. Graph the function by hand. Make your own grid below.
36.
f x( ) = x +1+ 3
fx
()
=x+1+3
Plot the points (0, 4), (3, 5), (8, 6), and (-1, 3) and draw a smooth curve through the points.
Solve each equation
37.
7− 8 2x −1 = −17
7-82x-1=-17
38.
2 x −1− 3x −1 = 0
2x-1-3x-1=0
39.
3t −1− 4t +1 = −1
3t-1-4t+1=-1
40. Sketch the graph of the function.
f x( ) = −2 x − 6( )2 − 2
fx
()
=-2x-6
()
2
-2
Plot the points (4, -10), (5, -4), (6, -2), (7, -4), and (8, -10)
41.
Sketch the graph of the function.
− x +1( )2 + 4
-x+1
()
2
+4
Plot the points (-4, -5), (-3, 0), (-1, 4), (1, 0), and (2, -5).
42. Find an equation of the function sketched below in the form:
43. Sketch by hand the graph of the function. Give the coordinates for the vertes.
f x( ) = x2 + 2x + 5
fx
()
=x
2
+2x+5
44. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 280 feet of fencing and does not fence along the
street, what is the largest area that can be enclosed?
45. Solve: (2x + 5)2 = 6
46.
Solve:
x + 5 2
⎛ ⎝⎜
⎞ ⎠⎟ 2
= 10 16
x+
5
2
æ
è
ç
ö
ø
÷
2
=
10
16
47.
Solve by completing the square:
x2 + 3x − 9 = 0
x
2
+3x-9=0
48.
Solve by completing the square:
6x2 + 6x + 7 = 6
6x
2
+6x+7=6
49.
Solve using the quadratic formula:
−3x2 + 2x = −4
-3x
2
+2x=-4
3x2 − 2x − 4 = 0
3x
2
-2x-4=0
50.
Solve using the quadratic formula:
−8x2 = −5x +1
-8x
2
=-5x+1
8x2 − 5x +1= 0
8x
2
-5x+1=0
