Question

dividing using synthetic division

(X cubed + 5X squared - X -9) divided by (X+2)

Answer 1

The zero of x+2 is -2, the coefficients of your polynomial are: 1, 5, -1 and -9.
That is all the information we need for the synthetic division:

Write them down this way, and drop the first coeff (1) right below the line:

-2 | 1 5 -1 9
|
+ ____________________
1

Multiply -2 with that 1 and write the result in the next column (below the 5). Add.

-2 | 1 5 -1 9
| -2
+ ____________________
1 3

Now multiply -2 with 3 and put the result in the next column. Add:

-2 | 1 5 -1 9
| -2 -6
+ ____________________
1 3 -7

Do the same again:

-2 | 1 5 -1 9
| -2 -6 14
+ ____________________
1 3 -7 23

Because the last sum is not 0, there is a remainder.
The other numbers (1, 3 and -7) are the coefficients of the second degree polynomial.

Result:

x²+3x-7 + 23/(x+2)

Answer 2

wow thank you so much

Answer 3

and do u know how to use synthetic division and the remainder theorem to find p(a) ?

Answer 4

wait how is the remainder 23? @ZeHanz

Answer 5

YOu have to divide x³+5x²-x-9 by x+2. If x+2 was a factor of x³+5x²-x-9, then there would be no remainder. The last number in the synth dev would be 0. Apparently, because this is not so (it is 23), there IS a remainder. it is 23. it still hase to be divided by x+2, so that is why the answer is x²+3x-7 + 23/(x+2)

Compare this with an ordinary long division of e.g. 23/7. The outcome is 3, remainder 2, because 3*7 +2 = 21 + 2 = 23.

One could say: 23/7 =3 + 2/7 = 3 2/7.

See? The remainder also has to be divided by 7.