Give an example of a division of a polynomial long division by a binomial and show all the steps when performing the division. The example must be your own and not from the text book. How is this similar to numerical division of real numbers? Give another

Polynomial division is very similar to long division that we learned in elementary school. Instead of simply using numbers, there are variables as well. The process, though, is effectively the same. We go through the problem term by term, just like in standard numerical long division. If we understand how to do one type of long division, it is quite easy to extend the technique to the other type of division. As long as we know how to multiply monomial terms with variables, the actual process is the same. The polynomial goes to the inside of the division symbol, and the binomial goes outside. We try to get the first term of polynomial from the binomial first term, and repeat this till we are able to get a polynomial of lesser degree than binomial (remainder) or till we get zero remainder. Example (x^2 + 5x + 6) divided by x + 5 We get X+5 /x^2 + 5x + 6 First we multiply by x to get x^2 + 5x We get X + 5/ x^2 + 5x + 6 -x^2 – 5x 6 We get the remainder as 6 Here quotient is x and the remainder is 6 If we divide same polynomial by x + 2 We get X+2 /x^2 + 5x + 6 First we multiply by x to get x^2 +2x, and then by 3 to get x + 6 We get X+5/ x^2 + 5x + 6 -x^2 – 2x X + 6 -x – 6 Zero remainder The quotient is x + 3 and remainder 0