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Questions and Answers
In this section, what operation will be done to polynomials?
In this section, what operation will be done to polynomials?
- Subtraction (correct)
- Addition (correct)
Add the following polynomials: 14x^2 - 8x + 3 and -6x^2 + 7x - 11. What is the result?
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?
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?
Add the following polynomials: -3x^2 - 2xy + y^2, -4x^2 - xy + 6y^2, and x^2 + 6xy - y^2. What is the result?
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?
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?
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?
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?
Subtract the following polynomials: 2x^2 + 5x - 10 from 3x^2 - x + 9. What is the result?
Subtract the following polynomials: 2x^2 + 5x - 10 from 3x^2 - x + 9. What is the result?
Subtract the following polynomials: (3.1x + 2.8z) - (4.3x - 1.2z). What is the result?
Subtract the following polynomials: (3.1x + 2.8z) - (4.3x - 1.2z). What is the result?
Subtract the following polynomials: (3m - 4n - 7) - (8m + n - 6). What is the result?
Subtract the following polynomials: (3m - 4n - 7) - (8m + n - 6). What is the result?
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?
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?
Perform the operation indicated: (6x^2 - 4x + 11) + (4 - x^2 - 3x). Write your answer in descending powers of x. What is the result?
Perform the operation indicated: (6x^2 - 4x + 11) + (4 - x^2 - 3x). Write your answer in descending powers of x. What is the result?
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?
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?
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?
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?
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?
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?
By how much does a^3 - 2a exceed a^2 + a - 6? What is the result?
By how much does a^3 - 2a exceed a^2 + a - 6? What is the result?
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?
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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