Help.... I am confused!?

Question

Given one of the terms, to find the additional terms, divide x+3 into the expression:

x^3 + 2x^2 - 5x -6 / x+3




Begin by dividing

Answer 1

....... ..x^2 - x - 2
...... -------------------------------------------------
x+3 | x^3 + 2x^2 - 5x - 6
........ x^3 + 3x^2
.........----------------
..................-x^2 - 5x
..................-x^2 - 3x
.................--------------
........................-2x. ..-...6
........................-2x.. .-.. 6
........................------------
............................. 0

Answer 2

I actually took a lot of time trying to do this, but instead of dividing through long division or synthetic division, we'll try factoring.

I haven't done this before, but it seems that it worked out just fine and I used the method complete the square instead this time it's complete the cube.

(a+b)^3=a^3+3a^2*b+3a*b^2+b^3
So then:
(x+b)^3=x^3+3x^2*b+3x*b^2+b^3
Now I let b=1
(x+1)^3=x^3+3x^2+3x+1

Now I'll try to make x^3+2x^2-5x-6 into (x+1)^3
You add by x^2+8x+7 also, suppose that x^3+2x^2-5x-6=0 to make it easier to factor.
x^3+3x^2+3x+1=x^2+8x+7
(x+1)^3=(x+1)(x+7)
(x+1)^2=(x+7)
x^2+2x+1-x-7=0
x^2-x-6=0
(x+3)(x-2)=0
Ignore the 0 part and you have gotten all the factors of the cubic equation.
(x+1)(x+3)(x-2)

So then you divide the entire thing by (x-3)
(x+1)(x-2) is your final answer.

Factoring is much more reliable in doing different things, doing division is less needed. Just my opinion.

Answer 3

Personally I favor long division. Let me see how well I can use the primitive graphics here (well, as it turns out, you'll have to use a little bit of imagination but if you know long division this will be nicer than it looks):

x^2 – x - 2
_______________
x+3|x^3 + 2x^2 - 5x – 6
x^3 + 3x^2
--------------
-x^2 – 5x
-x^2 – 3x
------------
-2x – 6
-2x – 6
---------
0

OK, so now you know that the division gives you

x^2 – x - 2

as one of the factors. This can be further factored as:

(x-2)(x+1)

and there you go!

Answer 4

Hello

This are hard to type in because they don't lione up nice.

x+3 into x^3 + 2x^2 -5x -6 = x^2 -1x -2 and this factors into (x-2)(x+1) and then our (x+3)

Hope This Helps!!

Answer 5

Using synthetic division to divide by
(x + 3) = (x - (-3)):-

**|1****2****-5****-6
-3|****-3*****3****6
---------------------------
***1***-1****-2****0
-------------------------

Gives:-
(x + 3).(x² - x - 2)
= (x + 3).(x - 2).(x + 1)