2-how-to-do-synthetic-division-mathbff

MIT grad shows how to do Synthetic Division. More videos with Nancy coming in 2017! Synthetic Division is a way to divide one polynomial by a linear expression (such as x+1 or x-3). Synthetic Division is often faster than long division with polynomials, if the polynomial you're dividing by is "x plus a number" or "x minus a number".

How to do synthetic division:

First draw a little corner symbol. Inside the corner, write the number that makes your denominator = zero. If your denominator is "x+1", you write -1 in the corner. Then write the coefficients of your top polynomial in a row to the right of the corner symbol. Leave space for another row and draw a horizontal line beneath that.

1) Drop down 1st coefficient number.

2) Multiply this number by corner constant.

3) Write product in 2nd column, 2nd row spot.

4) Add the two numbers in the 2nd column and write sum below the line in 2nd column.

5) Repeat steps until you have written a number in final column spot below line.

6) The new polynomial answer is formed from this bottom row of numbers. The 1st one is the leading coefficient. If the numbers are 1 4 3 2, the new polynomial is 1x^2 + 4x + 3 + 2/(x+1). Notice the last number is part of the remainder, and you put that number, 2, over the original divisor (x+1).

Tagged under: synthetic division,polynomial,divident,divisor,numerator,denominator,long division,remainder, ,column,row,leading coefficient,degree,algebra,algebra 2,precalculus,math,mathematics,khan,jmt,-,explanation,find,solution,test,tutor,tips,problem

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