DIVISION of a POLYNOMIAL between (x-a) BY RUFFINI METHOD STEP BY STEP

 The objective is to perform a division of a given polynomial among other polynomial type (x-a). Used in factoring a polynomial

Prerequisites: know the concept of polynomial, the concept of division and know the basic operations with integer numbers (addition, subtraction, multiplication and division).

   We are going to divide the polynomial x²+x-2 between the divisor polynomial x-1

To do this we will begin by drawing a couple of crossed lines and put left the a value, i.e. the value of the number that is subtracting to x in the divisor polynomial. In this case a is 1

then we write at the top of the drawing the coefficients of the polynomial ordered from the highest level to the lowest degree.. If missing some degree we would put a zero in its place. In this case the coefficients are 1, for x², 1 for x and -2, for -2.

Copy the first number above down the horizontal line

We multiply this number by the value of a (which is 1) and we put the result under the second number above

We add these two numbers and repeat multiplication

 

Now we add the last two numbers and put the result down. This will be the remaider (resto) of the division.

at this time we are able to construct the polynomial quotient of the division from the numbers that are under the horizontal line: 1 and 2, taking them as coefficients of this polynomial quotient

QUOTIENT = x²+2x

REMAINDER = 0

 

Then let's look at another example in video: