back to Unit 19

 

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