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Factor Theorem

A polynomial f(x) has a factor (x-c) if and only if f(x) = 0

Remainder Theorem

If a polynomial f(x) is divided by (x-c), the remainder is f(c)

put it over what you divided by

if a remainder occurs in long division what do you do

draw line change sings

what do you do when youre subtracting and adding underneath the divden

coefficents of the qutent

numbers below line on synthetic division are now what

what happens to the degree of the variables

begins at one less than the highest degree of the divined

if aksed to evaluate polynomials through direct and syntehtic subsuttion and given p(x) what do you do

direct- plug in the number | syntetic- put the number given on the outside of the L and the coefficents of the equation on the inside of the L and exceucte synthetic division

what does p=

factor of constant

what does q=

factor of lead coefficient

outside of synthetic dividison L

where do you place your p/q value

What is the Rational Zeros Theorem?

Every rational zero of P is of the form p/q