**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*;
*mx ^{4}*; 7

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: 4*mx*^{2}
+ *mx* 11

2*x*^{3}
+ 4*x* +7

8*y*
+ 8*x*

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: 4*mx*^{2 } 2mx^{2} 3*mx *+
*mx*
11

It becomes: 2* mx*^{2 } + -2*mx*
+ -11

Write these on the board: Try these:

Simplify:

1) 4*x *+ 4*x* 2) *st*
+15*st* 3)
-40*n *+ *n*

4) *ab* + 7*ab* 5) 6*jk*
*jk* 6)
72*mn* 20*mn*

7) -8*xy*^{2} 2*xy*^{2} + 3*xy* 4*y* 8) _{}*y* + 5*y* 4 +3

9) *uv*^{3} 7*uv* + 2*uv* + *v*
5 + 8 10) 5*x*^{2} + 4*y* 6 +
7*y*