Name ________________________________________ Date __________________ Class__________________
LESSON
Practice C
6-x
6-3
Polynomials
Find the degree and number of terms of each polynomial.
1. 5t 5 + 60 + 3t 3
2. 9p + 31p 9 + 6p 2 − 42
3. −50 + 4r − r 3 + r 2 − 4r 5
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Simplify and write each polynomial in standard form. Then, give
the leading coefficient.
4. 4g 3 + 8g − 4g 3 + 2g 2
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5. 13 − 5h 3 + h 2 − h
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6. 2( 3x + 4) − 4x + 8x
2
Classify each polynomial according to its degree and number of terms.
7. 6t 3 + 54t 4 − 1
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8. 14 • 3w + w
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9. 4( 4s 2 − s ) − 11 + s 7
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2
Evaluate each polynomial for the given value.
10. 4m − 4 − 4m 3 for m = −2
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11. 12y − 6y − 8y − y for y = −1
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7
2
12. −3a + a 3 −
3
1 2
a for a = 3
3
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13. A certain company’s profit in dollars can be modeled with the polynomial
−
1 2
x + 100x − 200 where x is the number of items produced and sold.
2
a. What is the profit if they produce and sell 10 of their products?
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b. What is the profit if they produce and sell 100 of their products?
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c. Evaluate the company’s profit polynomial for x = 0. What does this
number represent?
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
6-21
Holt McDougal Algebra 1
10. quadratic binomial 11. cubic polynomial
7. 3x 2 − x + 12; 3
12. 102 feet
8. −g 5 + g 4 − 2g 3 ; −1
4
3
2
9. k − k + k + 1; 1
Challenge
10. quadratic monomial 11. linear binomial
12. quartic trinomial
13. −3; 13; −2
2
14. 72 in
2. 2x 4 y 4 + 3x 2 y 5
3. x 5 + x 3 + x
4. 2xy + 5xz
5. 2x
4
7. 4x 2 − 3x 5 + x
Practice B
1. 3; 3
2. 2; 2
3
3. 4; 4
8
1. −3xy 4
2
4. 4x + 3x − x − 2; 4
5. 3j 3 − 4j 2 − 50j + 7; 3
9. quartic polynomial
11. 9
10. 4x 2 − 3x 2 y
11. x 2 + y 2 + z 2 + w 2
12. x 3 + x 2 + x
13. −3 + x + 4x 2
14. x 4 + x 3 + x 2
2. 2 s: 296 feet; 5 s: 500 feet
10. 7
3. UK: 146.25 feet; US: 194.4 feet
12. 10
4. h = 0.25: 0.9375 cubic feet;
h = 0.5: 1 cubic foot
5. A
Practice C
6. G
7. C
2. 9; 4
Reading Strategies
3. 5; 5
1. 3; 1
4. 2g 2 + 8g; 2
2. The exponents on the variables have a
sum of 4.
5. −5h 3 + h 2 − h + 13; −5
6. 8x 2 + 2x + 8; 8
7. quartic trinomial
8. quadratic binomial
9. 7th degree polynomial
10. 20
9. x y − 3xyz + z
1. 87.92 square centimeters
8. quartic trinomial
13. a. 187.5 m
b. 135.6 m
1. 5; 3
11. −9
3. cubic; binomial
4. −4g 2 + 8g + 1
5. −4
6. 2
7. trinomial
8. quadratic
6-4 ADDING AND SUBTRACTING
POLYNOMIALS
12. 15
13. a. $750
b. $4800
c. −200; It represents how much money
they will lose ($200) for not producing or
selling anything.
Practice A
Review for Mastery
1. 4x 3 − 6
2. –20p 5 − 3p + 14
3. 3m + 6
4. 5y 2 + y + 12
5. 6z 3 + 4z 2 + 5
6. 12g 2 + 4g − 1
7. 7x 3 + 6x
8. 8k + 1
3
9. 3s + 5s + 20
1. 8
2. 3
3. 4
4. 6
11. 9b 2 + b − 9
5. 5
6. 2
13. w + 8
9. 7x 2 + 8x −1; 7
14. a. 2n + 2
b. 8n + 20
c. 12n + 28
7. −6x 5 − 5x 4 + x 3 ; −6
8. −x 3 + 5x 2 + 2x; −1
8. x − 3
Problem Solving
6. 5k 4 − 4k 3 + 3k 2 + 6k; 5
7. quadratic binomial
6. 4xyz 2 + xyz
10. 9a 4 + 8a 2
12. 4c 3 + 6c
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A4
Holt McDougal Algebra 1