Operations on Polynomials

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!