5.E: Review Exercises and Sample Exam
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Review Exercises
Simplify.
- 73⋅76
- 5956
- y5⋅y2⋅y3
- x3y2⋅xy3
- −5a3b2c⋅6a2bc2
- 55x2yz55xyz2
- (−3a2b42c3)2
- (−2a3b4c4)3
- −5x3y0(z2)3⋅2x4(y3)2z
- (−25x6y5z)0
- Each side of a square measures 5x2 units. Find the area of the square in terms of x.
- Each side of a cube measures 2x3 units. Find the volume of the cube in terms of x.
- Answer
-
1. 79
3. y10
5. −30a5b3c3
7. 9a4b84c6
9. −10x7y6z7
11. A=25x4
Classify the given polynomial as a monomial, binomial, or trinomial and state the degree.
- 8a3−1
- 5y2−y+1
- −12ab2
- 10
- Answer
-
1. Binomial; degree 3
3. Monomial; degree 3
Write the following polynomials in standard form.
- 7−x2−5x
- 5x2−1−3x+2x3
- Answer
-
1. −x2−5x+7
Evaluate.
- 2x2−x+1, where x=−3
- 12x−34, where x=13
- b2−4ac, where a=−12,b=−3, and c=−32
- a2−b2, where a=−12 and b=−13
- a3−b3, where a=−2 and b=−1
- xy2−2x2y, where x=−3 and y=−1
- Given f(x)=3x2−5x+2, find f(−2).
- Given g(x)=x3−x2+x−1, find g(−1).
- The surface area of a rectangular solid is given by the formula SA=2lw+2wh+2lh, where l,w, and h represent the length, width, and height, respectively. If the length of a rectangular solid measures 2 units, the width measures 3 units, and the height measures 5 units, then calculate the surface area.
- The surface area of a sphere is given by the formula SA=4πr2, where r represents the radius of the sphere. If a sphere has a radius of 5 units, then calculate the surface area.
- Answer
-
1. 22
3. 6
5. −7
7. f(−2)=24
9. 62 square units
Perform the operations.
- (3x−4)+(9x−1)
- (13x−19)+(16x+12)
- (7x2−x+9)+(x2−5x+6)
- (6x2y−5xy2−3)+(−2x2y+3xy2+1)
- (4y+7)−(6y−2)+(10y−1)
- (5y2−3y+1)−(8y2+6y−11)
- (7x2y2−3xy+6)−(6x2y2+2xy−1)
- (a3−b3)−(a3+1)−(b3−1)
- (x5−x3+x−1)−(x4−x2+5)
- (5x3−4x2+x−3)−(5x3−3)+(4x2−x)
- Subtract 2x−1 from 9x+8.
- Subtract 3x2−10x−2 from 5x2+x−5.
- Given f(x)=3x2−x+5 and g(x)=x2−9, find (f+g)(x).
- Given f(x)=3x2−x+5 and g(x)=x2−9, find (f−g)(x).
- Given f(x)=3x2−x+5 and g(x)=x2−9, find (f+g)(−2).
- Given f(x)=3x2−x+5 and g(x)=x2−9, find (f−g)(−2).
- Answer
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1. 12x−5
3. 8x2−6x+15
5. 8y+8
7. x2y2−5xy+7
9. x5−x4−x3+x2+x−6
11. 7x+9
13. (f+g)(x)=4x2−x−4
15. (f+g)(−2)=14
Multiply.
- 6x2(−5x4)
- 3ab2(7a2b)
- 2y(5y−12)
- −3x(3x2−x+2)
- x2y(2x2y−5xy2+2)
- −4ab(a2−8ab+b2)
- (x−8)(x+5)
- (2y−5)(2y+5)
- (3x−1)2
- (3x−1)3
- (2x−1)(5x2−3x+1)
- (x2+3)(x3−2x−1)
- (5y+7)2
- (y2−1)2
- Find the product of x2−1 and x2+1.
- Find the product of 32x2y and 10x−30y+2.
- Given f(x)=7x−2 and g(x)=x2−3x+1, find (f⋅g)(x).
- Given f(x)=x−5 and g(x)=x2−9, find (f⋅g)(x).
- Given f(x)=7x−2 and g(x)=x2−3x+1, find (f⋅g)(−1).
- Given f(x)=x−5 and g(x)=x2−9, find (f⋅g)(−1).
- Answer
-
1. −30x6
3. 10y2−24y
5. 2x4y2−5x3y3+2x2y
7. x2−3x−40
9. 9x2−6x+1
11. 10x3−11x2+5x−1
13. 25y2+70y+49
15. x4−1
17. (f⋅g)(x)=7x3−23x2+13x−2
19. (f⋅g)(−1)=−45
Divide.
- 7y2−14y+287
- 12x5−30x3+6x6x
- 4a2b−16ab2−4ab−4ab
- 6a6−24a4+5a23a2
- (10x2−19x+6)÷(2x−3)
- (2x3−5x2+5x−6)÷(x−2)
- 10x4−21x3−16x2+23x−202x−5
- x5−3x4−28x3+61x2−12x+36x−6
- 10x3−55x2+72x−42x−7
- 3x4+19x3+3x2−16x−113x+1
- 5x4+4x3−5x2+21x+215x+4
- x4−4x−4
- 2x4+10x3−23x2−15x+302x2−3
- 7x4−17x3+17x2−11x+2x2−2x+1
- Given f(x)=x3−4x+1 and g(x)=x−1, find (f/g)(x).
- Given f(x)=x5−32 and g(x)=x−2, find (f/g)(x).
- Given f(x)=x3−4x+1 and g(x)=x−1, find (f/g)(2).
- Given f(x)=x5−32 and g(x)=x−2, find (f/g)(0).
- Answer
-
1. y2−2y+4
3. −a+4b+1
5. 5x−2
7. 5x3+2x2−3x+4
9. 5x2−10x+1+32x−7
11. x3−x+5+15x+4
13. x2+5x−10
15. (f/g)(x)=x2+x−3−2x−1
17. (f/g)(2)=1
Simplify.
- (−10)−2
- −10−2
- 5x−3
- (5x)−3
- 17y−3
- 3x−4y−2
- −2a2b−5c−8
- (−5x2yz−1)−2
- (−2x−3y0z2)−3
- (−10a5b3c25ab2c2)−1
- (a2b−4c02a4b−3c)−3
- Answer
-
1. 1100
3. 5x3
5. y37
7. −2a2c8b5
9. −x98z6
11. 8a6b3c3
The value in dollars of a new laptop computer can be estimated by using the formula V=1200(t+1)−1, where t represents the number of years after the purchase.
- Estimate the value of the laptop when it is 112 years old.
- What was the laptop worth new?
- Answer
-
2. $1,200
Rewrite using scientific notation.
- 2,030,000,000
- 0.00000004011
- Answer
-
2. 5.796×1019
Perform the indicated operations.
- (5.2×1012)(1.8×10−3)
- (9.2×10−4)(6.3×1022)
- 4×10168×10−7
- 9×10−304×10−10
- 5,000,000,000,000×0.0000023
- 0.0003120,000,000,000,000
- Answer
-
2. 5.796×1019
4. 2.25×10−20
6. 2.5×10−18
Simple Exam
Simplify.
- −5x3(2x2y)
- (x2)4⋅x3⋅x
- (−2x2y3)2x2y
-
- (−5)0
- −50
- Answer
-
1. −10x5y
3. 4x2y5
Evaluate.
- 2x2−x+5, where x=−5
- a2−b2, where a=4 and b=−3
- Answer
-
1. 60
Perform the operations.
- (3x2−4x+5)+(−7x2+9x−2)
- (8x2−5x+1)−(10x2+2x−1)
- (35a−12)−(23a2+23a−29)+(115a−518)
- 2x2(2x3−3x2−4x+5)
- (2x−3)(x+5)
- (x−1)3
- 81x5y2z−3x3yz
- 10x9−15x5+5x2−5x2
- x3−5x2+7x−2x−2
- 6x4−x3−13x2−2x−12x−1
- Answer
-
1. −4x2+5x+3
3. −23a2−59
5. 2x2+7x−15
7. −27x2y
9. x2−3x+1
Simplify.
- 2−3
- −5x−2
- (2x4y−3z)−2
- (−2a3b−5c−2ab−3c2)−3
- Subtract 5x2y−4xy2+1 from 10x2y−6xy2+2.
- If each side of a cube measures 4x4 units, calculate the volume in terms of x.
- The height of a projectile in feet is given by the formula h=−16t2+96t+10, where t represents time in seconds. Calculate the height of the projectile at 112 seconds.
- The cost in dollars of producing custom t-shirts is given by the formula C=120+3.50x, where x represents the number of t-shirts produced. The revenue generated by selling the t-shirts for $6.50 each is given by the formula R=6.50x, where x represents the number of t-shirts sold.
- Find a formula for the profit. (profit = revenue − cost)
- Use the formula to calculate the profit from producing and selling 150 t-shirts.
- The total volume of water in earth’s oceans, seas, and bays is estimated to be 4.73×1019 cubic feet. By what factor is the volume of the moon, 7.76×1020 cubic feet, larger than the volume of earth’s oceans? Round to the nearest tenth.
- Answer
-
1. 18
3. y64x8z2
5. 5x2y−2xy2+1
7. 118 feet
9. 16.4