Questions and Answers
In this section, what operation will be done to polynomials?
Add the following polynomials: 14x^2 - 8x + 3 and -6x^2 + 7x - 11. What is the result?
8x^2 - x - 8
Add the following polynomials: -4.1x^2 + 0.9x - 9.8 and 1.7x^2 - 2.4x - 1.6. What is the result?
-2.4x^2 - 1.5x - 11.4
Add the following polynomials: -3x^2 - 2xy + y^2, -4x^2 - xy + 6y^2, and x^2 + 6xy - y^2. What is the result?
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Add the following polynomials: 2x^3 - 4x^2 + 6x - 3, x^3 + 6x^2 - 8x + 12, and -3x^3 + 2x^2 - 4x - 7. What is the result?
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Add the following polynomials: x^4 - 3x + 1, 4x^2 - 2x + 8, and x^3 - 9. Write your answer in descending powers of x. What is the result?
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Subtract the following polynomials: 2x^2 + 5x - 10 from 3x^2 - x + 9. What is the result?
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Subtract the following polynomials: (3.1x + 2.8z) - (4.3x - 1.2z). What is the result?
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Subtract the following polynomials: (3m - 4n - 7) - (8m + n - 6). What is the result?
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Subtract the following polynomials: Subtract 2x^2 - 6x - 4 from 4x^2 - 4x + 3. Write your answer in descending powers of x. What is the result?
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Perform the operation indicated: (6x^2 - 4x + 11) + (4 - x^2 - 3x). Write your answer in descending powers of x. What is the result?
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Perform the operation indicated: (a^3 - 2a + 5) - (4a^3 - 5a^2 + a - 2). Write your answer in descending powers of a. What is the result?
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Perform the operation indicated: (5m^3 + 3mn^2) + (-7m^2n + mn^2 - n^3) - (mn^2 + 2m^3). Write your answer in descending powers of m. What is the result?
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What must be added to 3x - 7 to make x^2 + 4x - 1? Write your answer in descending powers of x. What is the result?
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By how much does a^3 - 2a exceed a^2 + a - 6? What is the result?
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Perform the indicated operation: The perimeter of a triangle is 7a - 11b. If two of its sides are 2a + b and a - 9b, what is the third side? What is the result?
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Study Notes
Polynomial Addition and Subtraction
- Operations performed on polynomials include both addition and subtraction.
- Addition combines like terms to form a new polynomial.
- Subtraction involves subtracting coefficients of like terms.
Examples of Polynomial Addition
- Adding (14x^2 - 8x + 3) and (-6x^2 + 7x - 11) results in (8x^2 - x - 8).
- Combining (-4.1x^2 + 0.9x - 9.8) with (1.7x^2 - 2.4x - 1.6) yields (-2.4x^2 - 1.5x - 11.4).
- Adding polynomials (-3x^2 - 2xy + y^2), (-4x^2 - xy + 6y^2), and (x^2 + 6xy - y^2) gives (-6x^2 + 3xy + 6y^2).
Examples of Polynomial Subtraction
- Subtracting (3x^2 - x + 9) from (2x^2 + 5x - 10\ results in (-x^2 + 6x - 19).
- Performing ((3.1x + 2.8z) - (4.3x - 1.2z)) simplifies to (-1.2x + 4.0z).
- Subtracting ((3m - 4n - 7) - (8m + n - 6)) results in (-5m - 5n - 1).
Advanced Polynomial Operations
- To find the resultant polynomial (5x^2 - 7x + 15), combine ((6x^2 - 4x + 11) + (4 - x^2 - 3x)).
- The subtraction of (2x^2 - 6x - 4) from (4x^2 - 4x + 3\ gives (2x^2 + 2x + 7).
- The expression (-3a^3 + 5a^2 - 3a + 7\ results from subtracting (4a^3 - 5a^2 + a - 2) from (a^3 - 2a + 5).
Working with Unknowns
- To find what must be added to (3x - 7) to equal (x^2 + 4x - 1), the result is (x^2 + x + 6).
- To determine how much (a^3 - 2a) exceeds (a^2 + a - 6), the expression is (a^3 - a^2 - 3a + 6).
Application in Geometry
- Understanding the perimeter of a triangle given (7a - 11b) and two sides (2a + b) and (a - 9b) leads to the third side being (4a - 3b).
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Description
This quiz focuses on addition and subtraction operations with polynomials, typical for Algebra II assignments. Students will need to demonstrate their understanding by solving several polynomial problems, including combining like terms and placing results appropriately. Use this quiz to reinforce your skills in working with polynomials.
