Operations with Polynomials

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The following math revision questions are provided in support of the math tutorial on Operations with Polynomials. In addition to this tutorial, we also provide revision notes, a video tutorial, revision questions on this page (which allow you to check your understanding of the topic) and calculators which provide full, step by step calculations for each of the formula in the Operations with Polynomials tutorials. The Operations with Polynomials calculators are particularly useful for ensuring your step-by-step calculations are correct as well as ensuring your final result is accurate.

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11.2Operations with Polynomials

Operations with Polynomials Revision Questions

1. . Which of the following terms is not like the others?

1. 5x5yz3
2. -3x5yz3
3. 5xy5z3
4. x5yz3

2. . What is the leading coefficient in the polynomial

P(x) = 3 - 4x - 5x2
1. 3
2. -4
3. -5
4. 5

3. . What is the leading term in the polynomial

P(x) = 3x - 4x2 - 1
1. 3x
2. -4
3. -4x2
4. -1

4. . What is the polynomial S(x) resulting from the division of P(x) = x2 - 5x - 6 and Q(x) = x + 1?

1. S(x) = x + 6
2. S(x) = x - 6
3. S(x) = x - 7
4. S(x) = x + 7

5. . If P(x, y) = 3x2y + 4xy - xy2 and Q(x) = xy/2, then what is P(x)/Q(x)?

1. 6x - 2y + 8
2. 3x - y + 4
3. 3x/2 - y/2 + 2
4. 6x3y2 - 2x2y3 + 8x2y2

6. . If Q(x) = x2 - 2x + 1 and S(x) = x - 1, then what is P(x) if S(x) = P(x)/Q(x)?

1. P(x) = x3 - 3x2 + 3x - 1
2. P(x) = x3 - 3x2 - 3x + 1
3. P(x) = x - 1
4. P(x) = x3 - 1

7. . What is the standard form of the polynomial

P(x) = 5x3 y - 4xy - 2xy3 - x2 y2 + 7xy - 2x3 y + x2 y2 - 3x3 y
1. P(x) = 3x3y + 4xy3
2. P(x) = 5x3y + 3xy
3. P(x) = 2xy3 - 3xy
4. P(x) = -2xy3 + 3xy

8. . What is [P(x)]2 if P(x) = 2xy + y2?

1. 4x2y2 + 4xy3 + y4
2. 4x2y + 4xy2 + y3
3. 4x2y2 + y4
4. 2x2y2 + y4

9. . If P(x) = 12x3y4Z2 and Q(x) = 4x2yz, then what is P(x)/Q(x)?

1. 3xyz
2. 3xy3z
3. 4xyz3
4. 3xyz3

10. . What is/are the zero(es) of the polynomial P(x) = x3 - 4x?

1. 0 only
2. -2 and 0
3. -2 and 2
4. -2, 0 and 2

11. . What are the zeroes of the polynomial shown by the graph line in the figure?

1. -10.4 and 10.4
2. -3.5, 0 and 3.5
3. -3, 0 and 3
4. -10.4, 0 and 10.4

12. . How many zeroes does the polynomial shown in the graph have?

1. 4
2. 3
3. 2
4. 1

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2. Polynomials Math tutorial: Operations with Polynomials. Read the Operations with Polynomials math tutorial and build your math knowledge of Polynomials
3. Polynomials Video tutorial: Operations with Polynomials. Watch or listen to the Operations with Polynomials video tutorial, a useful way to help you revise when travelling to and from school/college
4. Polynomials Revision Notes: Operations with Polynomials. Print the notes so you can revise the key points covered in the math tutorial for Operations with Polynomials
5. Check your calculations for Polynomials questions with our excellent Polynomials calculators which contain full equations and calculations clearly displayed line by line. See the Polynomials Calculators by iCalculator™ below.
6. Continuing learning polynomials - read our next math tutorial: Solutions for Polynomial Equations

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