please help, show your work?

Question

x squared+6 divided by x+3

Answer 1

(x^2 + 6) / (x + 3) is already in simplest form. A quick visualization of the graph of x^2 + 6 will show you that it lies completely above the x-axis, and therefore has no zeroes, and thus no factors, so x + 3 cannot be a factor of it, and there is no way to simplify it.

If you're supposed to do long division, then you get 1*x in the x place, and the new dividend is -3x + 6. That gives you -3 in the ones place, and a remainder of 15. So it's x - 3, remainder 15.

Answer 2

If you are wanting to reduce the fraction, it is reduced to it's lowest form.

If you actually want to simplify, you must either use long division or use synthetic division.

In either case, be sure to list any power that is not included in your problem with a zero.

For instance, your numerator skips x to the first power, so you'll want to write it as x squared + 0x + 6, prior to actually dividing with either of the aforementioned methods.

Answer 3

umm, well this is kind of hard to do over the internet, but u can use a form of long division note: im putting in 0x, b/c it makes it easier, ignore teh underscores (_):

(x+3) | (x^2+0x+6)

(times the divisor [x+3] by x, and subtract from first two terms in divedend [x^2+3], then bring down the 6)

_________x <--- write what you're muliplying up here
(x+3) | (x^2+0x+6)
-_____x^2+3x
=________-3x+6


(then multiply the divisor by -3, subtract from dividend, the first three lines are as from before**)

_________x_-3 <---------!!
(x+3) | (x^2+0x+6)
-_____x^2+3x
=________-3x+6
-_________-3x-9
=___________-3 <--this is your remainder

THEREFORE, when x^2+6 id divided by x+3 the result is x-3 with a remainder of -3, or:
(x^2+6)=(x+3)(x-3)-3

Answer 4

Use synthetic division to solve.

For an easy lesson, go to:

http://www.purplemath.com/modules/synthdiv.htm

Guido