### Video instructions and help with filling out and completing How Form 5495 Index Instructions and Help about How Form 5495 Index

What are the different types of polynomials let's say we have a polynomial like 4x plus X cubed plus 3 plus 7 X raise to 5 it's a higher order polynomial because we have an order higher than - does it look a bit weird perhaps you can say that it does not look perfect we should always write a polynomial in the descending order of the powers of its terms 5 is the highest power among these 4 terms which is why we write 7 X raise to 5 first then we have the power 3 we write X cubed next and then 4 X + 3 so we wrote the polynomial as 7 X raise to 5 plus X cubed + 4 X + 3 this is called the standard form of the polynomial this is one of the most important forms we need to understand as it is used for factorization as well as division of polynomials look at the standard form do you see that a few powers of X are missing in between what I am really talking about is all the non-negative powers under the highest power 5 we have 5 3 1 and 0 which means that the powers 4 & 2 are missing that brings us to the index form where we include all non-negative powers of X which are less than 5 we write 7 X raised to 5 as is but how do we include the power 4 it's simple we add 0 X raise to 4 we're not changing the value of the polynomial here since we are adding a 0 then we write X cubed as is we have covered 5 4 & 3 what remains is 2 1 and 0 as we do not have a 2 we add 0 X raise to 2 we already have a 1 and a 0 so we write 4 X +3 as is the index form covers all the non negative powers of X lower than the highest power five four three two one and zero remember this is 3 X raised to 0 the index form gives us the answer to another form which is the coefficient form as the name suggests it only considers the coefficients of each term what are the coefficients of each term in the index form the coefficient of x raise to 5 is 7 the coefficient of x raise to 4 is 0 the coefficient of x raise to 3 is 1 and so on in the coefficient form they can be written as 7 0 1 0 4 and three coefficients written within brackets is called the coefficient form the highest power of the polynomial is called the degree of the polynomial 5 is the highest power in this polynomial and that's the reason 5 is the degree of the polynomial next we will look at a few more examples of these forms you