basic math notes

polynomials can have just variables, just constants or both
polynomial = only uses +- or *
non negative integers

DEGREE OF A TERM = the sum of exponents of all variables --6y^7x^4  degree is 7+4 = 11
gotcha if theres only a constant then the degree is ZERO, 1/2 the degree is zero etc
x^0 = 1

DEGREE OF A POLYNOMIAL= 7-3x+8x^3y =
            (0)(1)+(3)(1) = 1+3 = add 1+3 = 4 degree of polynomial = 4

STANDARD FORM OF A POLYNOMIAL = Terms in order from highest to lowest degree

SIMPLIFYING TERMS SHORTCUTS EXPONENTS
MULTIPLICATION
2*2*2*2*2 = 2*5
EXPONENTS
2^5  2 is the base 5 is the exponent

(-3)^4 = 81
-3^4 = -81....-1*3^4
P(arenthesis)E(xponent)M(ultiplication)D(ivision)A(ddition)S(ubtraction)

2(-2^2) = -8...-2*-2= 4*-1= -4*2= -8

3^2*3^4 = 3^6

a^b+a^c= a^b+c

x^5*3^2*y^3*x^8 = 9x^13y^3
y^4 x^2 y^-2 = y^2 x^2

negative exponents are actually veiled ways of writing division
find the factor with negative exponent and move it underneath the factors with positive exponents then flip the sign of exponent

inverse simplification

example x^2 y^4 y^-2 = x^2y^4   or x^-a = 1      ex. 3y^-1x^3  = 3x^3
               -------        --            ------
            y^2       x^a                      y