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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:

Simplify:

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