Curriculum Outcomes
Patterns and Relations: Represent algebraic expressions in multiple ways.
5. Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2). [C, CN, R, V]
6. Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree less than or equal to 2). [C, CN, PS, R, V]
7. Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially and symbolically. [C, CN, R, V]
Patterns and Relations: Represent algebraic expressions in multiple ways.
5. Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2). [C, CN, R, V]
6. Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree less than or equal to 2). [C, CN, PS, R, V]
7. Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially and symbolically. [C, CN, R, V]
Things You Need to Know
- Monomials are a product of a bunch of numbers and variables ("letters").
- (examples: 3, x, 8x, 24xy)
- Monomials are sometimes called "terms".
- Polynomials are a sum of a bunch of monomials.
- (examples: (2x + 4), (x + 15y - 23), (12xy + 45x - 14y + 5))
- Binomials are polynomials where the sum is of only two monomials.
- (examples: (20x + 40), (15y + 5x))
- Trinomials are polynomials where the sum is of three monomials.
- (examples: (3x + 8y - 4), (4a - 6b + 19ab))
- "Coefficient" means "the number that is multiplying the variable".
- In the monomial 5xy, the coefficient is 5.
- The degree of a monomial can be found by adding the exponents on all the variables in that monomial.
- The degree of 5(x^5)(y^2)(z) would be 5 + 2 + 1 = 8.
- The degree of a polynomial is simply the degree of the monomial in that polynomial that has the highest degree.
- "Like terms" means monomials that have the exact same type of variables.
- 9xy, 4xy, -xy, and 14xy all have "like terms".
- In order to add polynomials:
- Identify like terms.
- For each set of like terms, add the coefficients and keep the variables the same.
- In order to subtract polynomials:
- Change the sign of each term of the second polynomial.
- If you have (9x + 3y) - (6x - 2y), this becomes: 9x + 3y - 6x + 2y
- Then collect your like terms.
- Change the sign of each term of the second polynomial.
- In order to multiply monomials x monomials:
- Multiply the coefficients.
- Add the exponents on identical variable bases.
- Any variables that aren't matching with others just stay the same.
- Example: (4xy)(3y^2) = (12xy^3)
- In order to divide monomials / monomials:
- Divide the coefficients.
- Subtract the exponents.
- Any variables that aren't match with others just stay the same.
- In order to multiply monomial x polynomial:
- The monomial must multiply each term in the polynomial.
- Operation signs (+ or -) will stay the same.
- Example: (4x)(6x + 7) = (24x^2 + 28x)
- In order to divide polynomial / monomial:
- The monomial must divide each term in the polynomial.
- Again, operation signs will stay the same.
Interactive Activities
- Battleship - game of Battleship for practicing adding/subtracting polynomials
Class Notes