Math Notes on Polynomials
Write these notes on the board and have students copy
Monomial: An expression that is a number, variable or a product of a number and one or more variables with a whole number exponent
Examples: -11; k; mx4; 7p2f
A monomial that contains no variables is a constant
Polynomial: An expression that sums more than one monomial (or term), it is written from greatest to least exponents.
Examples: 4mx2 + mx 11
2x3 + 4x +7
8y + 8x
Terms that differ only by their coefficients are like terms
If terms differ by their exponents they are different terms and cannot be combined!
Remember: monomials and polynomials are expressions (they do not contain any equal sign!)
Simplifying polynomials: To simplify a polynomial, you combine like terms. Remember all constants can be combined (they are not considered terms).
Remember to write all subtraction as addition of a negative number, see the example below:
Simplify: 4mx2 2mx2 3mx + mx 11
It becomes: 2 mx2 + -2mx + -11
Write these on the board: Try these:
1) 4x + 4x 2) st +15st 3) -40n + n
4) ab + 7ab 5) 6jk jk 6) 72mn 20mn
7) -8xy2 2xy2 + 3xy 4y 8) y + 5y 4 +3
9) uv3 7uv + 2uv + v 5 + 8 10) 5x2 + 4y 6 + 7y