austin1250 said:Can anyone explain the correct way to do that type of long division with functions?
If you don't get what i mean an example would be like
x4+3x2+1 / x2-2x+3
To perform long division of functions, you first need to arrange the functions in a division format, with the dividend on top and the divisor on the bottom. Then, you will need to use the distributive property to divide each term of the dividend by the divisor. Finally, simplify the resulting expression by combining like terms and factoring, if necessary.
The purpose of long division of functions is to simplify complex expressions involving functions. It allows us to break down a complicated expression into smaller, more manageable parts. This can make it easier to evaluate or graph the function, or to find the domain and range.
Long division of functions is typically used when the functions involved are polynomials. It is especially helpful when the degree of the divisor is higher than the degree of the dividend, as it allows us to write the quotient in a simplified form.
Some common mistakes to avoid include making errors in the distributive property, not simplifying the resulting expression, and forgetting to include all terms in the quotient. It is important to double check your work for accuracy and to carefully follow the steps in the long division process.
Long division of functions can be used for most types of functions, as long as they can be written in polynomial form. However, it may not be the most efficient method for dividing certain types of functions, such as rational functions. In these cases, other methods such as synthetic division may be more appropriate.