Operations on Polynomials

Questions and Answers

What is the result of subtracting 5a^2 - 2a from 7a^2 + 5a + 6?

2a^2 + 7a + 6

What is the product of -2a and 5a^2?

-10a^3

What is the result of multiplying (m^2 - 5) by (m^3 + 2m - 2)?

m^5 - 3m^3 - 2m^2 - 10m + 10

What is the sum of 3m^2n + 5mn^2 - 7mn and 2m^2n - mn^2 + mn?

<p>5m^2n + 4mn^2 - 6mn</p> Signup and view all the answers

Study Notes

Operations on Polynomials

Addition, subtraction, multiplication, and division of polynomials follow similar rules as algebraic expressions.

Subtraction Example

To subtract polynomials, rearrange and combine like terms.
Example calculation:
- Subtract (5a^2 - 2a) from (7a^2 + 5a + 6) results in:
- ( (7a^2 + 5a + 6) - (5a^2 - 2a) = 2a^2 + 7a + 6 )

Multiplication Example

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial.
Example calculation:
- Multiply (-2a) by (5a^2) yields:
- (-2a \times 5a^2 = -10a^3)

Polynomial Product Example

Multiplying two polynomials requires distributing each term in one polynomial by each term in the other.
Example calculation:
- For ((m^2 - 5) \times (m^3 + 2m - 2)):
- Distributing gives:
  - ( m^5 + 2m^3 - 2m^2 - 5m^3 - 10m + 10 )
- Combining like terms results in:
  - ( m^5 - 3m^3 - 2m^2 - 10m + 10 )
- Degree of the resulting polynomial is 5.

Addition Example

Adding polynomials involves rearranging and combining like terms.
Example calculation:
- Adding (3m^2n + 5mn^2 - 7mn) and (2m^2n - mn^2 + mn):
- Results in:
  - ( 5m^2n + 4mn^2 - 6mn ) after arranging and combining like terms.

Description

This quiz covers the fundamental operations on polynomials, including addition, subtraction, multiplication, and division. Students will solve problems and simplify expressions using these operations effectively. Get ready to test your understanding of polynomial manipulation!