Question

Create your own division of polynomials problem. Demonstrate how this problem would be solved using both long division and synthetic division. I do not get this at all....

Answer 1

well I did the same question as you and this is my work if you want to copy it I don't mind.

1) (x+2)^3 - 4
---------------- = (x + 2)^2 with a remainder of -4.
(x+2)

----------------------------------
2)

(x + 2) * (x + 3) * (x + 4) = x^3 + 9x^2 + 26x + 24

So let's divide x^3 + 9x^2 + 26x + 24 by (x + 2)

Long division first:

. . . . . .x^2 + 7x + 12
. . . . .---------------------------------------…
x + 2 | x^3 + 9x^2 + 26x + 24
. . . . . x^3 + 2x^2
. . . . -----------------
. . . . . . . . . . 7x^2 + 26x
. . . . . . . . . . .7x^2 + 14x + 24
. . . . . . . . . ---------------------------
. . . . . . . . . . . . . . . . 12x + 24
. . . .. . . . . . . . . . . . . 12x + 24
. . . . . . . . . . . . . . . . -----------------
. . . . . . . . . . . . . . . . . . . . . . 0 <----------- remainder


Since x^2 + 7x + 12 = (x + 3) * (x + 4) we know that this is correct.
--------------------

Synthetic Division


-2 | 1 9 26. 24. . . . . . . . . (because (x+2) = 0 implies x = -2
| . . -2 -14. -24
------------------------------
. . .1. 7. 12. 0

This (1 7 12 0) is read as x^2 + 7x + 12 with a remainder of 0

Same answer as long division. Notice that I multiplied the 1 by (-2), the 7 by (-2) and the 12 by (-2)

Answer 2

@LillieMax does this help

Answer 3

Yes yes this does. Thanks so so much xD .

Answer 4

yw