Use synthetic division to divide 5x³ - x² + 6 by x - 4 .

Solution

Okay along with synthetic division we pretty much avoid all the x's and just work with the numbers in the polynomials.

Primary, let's notice that in this case r=4.

Now we have to set up the procedure. There are various different notations for doing this. We'll be utilizing the following notation.

In the polynomial the numbers to right of the vertical bar are the coefficients of the terms written in order of diminishing exponent. Also consider that any missing terms are acknowledged along a coefficient of zero.

Now, it will possibly be easier to write down the procedure and then described it so here it is.

First thing we do is fall the first number in the top line straight down as illustrated.  Then along each of the diagonal we multiply the starting number by r (that is 4 in this case) and put this number in the second row.  At last, add the numbers within the first & second row putting the results into the third row.  We continue this till we get attained the final number in the first row.

Now, notice that the numbers in the bottom row are the coefficients of the quadratic polynomial from our answer written in order of decreasing exponent and the final number in the third row is the remainder.

Then the answer is the same as example.

5x³ - x² + 6 = (x - 4) (5x²  + 19 x + 76 = 310