Simplify Using Long Division or Synthetic Division?

Question

Well you can't use synthetic division b/c its x^2 in the problem here's the problem
(x^3+8x^2-3x+16) divide by (x^2 + 5)

LoL its complicated i hear yah b/c i get to only have
-8x - 24 and how do you get x^2 into -8x ?? lol..

or would you just have
x + 8 + -8x (-24/x^2+5) ?????

whoops ( around -8x too lol..

Answer 1

Dividend: x²(x+8)(-3x+16)
divisor: (x²+5)
quocient: -x-8
remainder: -8x - 24
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Answer 2

guy made branch purely works with linear divisors (because you're applying the basis / 0 of a linear expression). To divide applying long branch: First, take x^4 and divide it by using x^2 (maximum well known term ÷ maximum well known term). You get x^2. *** x^2 as a result's the 1st term interior the quotient *** Multiply what you acquire (x^2) by using what you're dividing by using (x^2 - 3) to get x^4 - 3x^2, then subtract from x^4 + x^2 - 2x + a million .·. x^4 + x^2 - 2x + a million - (x^4 - 3x^2) = 4x^2 - 2x + a million. Now you're dividing 4x^2 - 2x + a million by using x^2 - 3. back, take the 4x^2 and divide by using x^2 (maximum well known term ÷ maximum well known term). you will get 4. *** 4 is the subsequent term interior the quotient *** Multiply what you acquire (4) by using what you're dividing by using (x^2 - 3) to get 4x^2 - 12, then subtract from 4x^2 - 2x + a million .·. 4x^2 - 2x + a million - (4x^2 - 12) = -2x + 13. because -2x + 13 is of a smaller degree than x^2 - 3, we are achieved. -2x + 13 is something, and the quotient is: x^2 + 4 the rest -2x + 13 OR x^2 + 4 + (-2x + 13)/(x^2 - 3) to learn, write the expression x^2 + 4 + (-2x + 13)/(x^2 - 3) applying a uncomplicated denominator. it particularly is going to be (x^4+x^2-2x+a million) / (x^2-3)

Answer 3

It's difficult to show synthetic long division on here, but your quotient should be (x + 8) and your remainder should be (-8x - 24)