Polynomial Synthetic Division Math Is Fun

And we could simplify this by using traditional algebraic long division.

Polynomial synthetic division math is fun. A polynomial can have constants variables and exponents but never division by a variable. 2x 2 5x 1 divided by x 3. The synthetic division is a shortcut way of polynomial division especially if we need to divide it by a linear factor. Then the highlighted parts were reduced 6 3 2 and 3 3 1 to leave the answer of 2x 1.

Synthetic division is generally used however not for dividing out factors but for finding zeroes or roots of polynomials. More about this later. It has fewer steps to arrive at the answer as compared to polynomial long division method. Reverse the sign of the constant term in the divisor.

Q x is 2x 1. Divide the first term of the numerator by the first term of the denominator and put that in the answer. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors. If you need to divide by a polynomial with a higher degree or one that doesn t have a 1 as the leading coefficient you ll have to do plain old long division.

Synthetic division is a shorthand or shortcut method of polynomial division in the special case of dividing by a linear factor and it only works in this case. In other words change 2 in x 2 into 2 and bring it down. Thus the formal definition of synthetic division is given as. Sometimes it is easy to divide a polynomial by splitting it at the and signs like this press play.

In this expression we re dividing this third degree polynomial by this first degree polynomial. X 2 x 5x 2x 24. Divide x 3 5x 2 2x 24 by x 2. But what we re going to cover in this video is a slightly different technique and we call it synthetic division.

Multiply the denominator by that answer put that below the numerator. In this lesson i will go over five 5 examples that should hopefully make you familiar with the basic procedures in successfully dividing polynomials using synthetic division. R x is 2. When the polynomial was split into two parts we still had to keep the 3 under each one.

Also they can have one or more terms but not an infinite number of terms. Synthetic division can only be used if you re dividing by a linear factor in the form x a. 2 1 5 2 24. How to do synthetic division when the degree of the polynomial is 3.

Repeat using the new polynomial. But you need to know one more thing. F x is 2x 2 5x 1. I must say that synthetic division is the most fun way of dividing polynomials.

For example it works if you are dividing by x 3 or by x 4. In the style f x d x q x r x we can write. Subtract to create a new polynomial. 2x 2 5x 1 x 3 2x 1 2.