Help me complete this polynomial equation?

Question

undeadknight26 · Answer

x=6
-6  -6
x-6=0

x=-2
+2 +2
x+2=0

x=-7
+7  +7
x+7=0
	
Then:

(x-6)(x+2)(x+7)=0
(x^2-4x-12)(x+7)=0
x^3-11x^2+16x+84=0

undeadknight26 · Answer

Also identify if there are any mistakes.

undeadknight26 · Answer

@iambatman @iGreen

igreen · Answer

I believe you made a mistake..$x^3-11x^2+16x+84=0$ gives me $x = -2, 6, 7$.

igreen · Answer

You expanded wrong..expand it again and see what you get.

undeadknight26 · Answer

Dude i have no idea how to do anything ;-;

joel_the_boss · Answer

@Mr.Booker_OCVS    xD   

Imagine

igreen · Answer

Erm, okay.. c:

$(x-6)(x+2)(x+7)$

Let's separate (x - 6)(x + 2) from (x + 7) and multiply them separately:

$(x-6)(x+2)$

$x^2 + 2x - 6x - 12$

Simplify:

$x^2 - 4x - 12$

Now we plug this back in and replace (x - 6)(x + 2) with x^2 - 4x - 12:

$(x^2 - 4x - 12)(x + 7)$

Can you multiply that? @undeadknight26

undeadknight26 · Answer

@Joel_the_boss i would kill myself if any of those teachers were on this site ._.

igreen · Answer

Can you?

igreen · Answer

$(x^2 - 4x - 12)(x + 7)$

$x^2 \times x$
$x^2 \times 7$

$-4x \times x$
$-4x \times 7$

$-12 \times x$
$-12 \times 7$

undeadknight26 · Answer

So really it WAS just the last step that was wrong eh?

igreen · Answer

I don't know..lol.

igreen · Answer

Can you just multiply the trinomial with the binomial already? :P

igreen · Answer

And yep, it was the last step :P

igreen · Answer

??

@undeadknight26

undeadknight26 · Answer

shush =.=

x^3 + x^2 - 40x - 84

undeadknight26 · Answer

Sorry that took so long my computer is a piece of...grabage ._.

igreen · Answer

Lol..

Okay, you still made one mistake..

igreen · Answer

I get:

$x^3 + 7x^2 - 4x^2 - 28x - 12x - 84$

Subtract -28x - 12x:

$x^3 + \color{red}{7x^2 - 4x^2} - 40x - 84$

Here's where you went wrong..subtract that..what do you get? @undeadknight26

undeadknight26 · Answer

3x?

undeadknight26 · Answer

@iGreen ?

igreen · Answer

$3x^2$*

igreen · Answer

So what's your final answer going to be? @undeadknight26

undeadknight26 · Answer

x=6
-6  -6
x-6=0

x=-2
+2 +2
x+2=0

x=-7
+7  +7
x+7=0
	
Then:

(x-6)(x+2)(x+7)=0
(x^2-4x-12)(x+7)             
x^3 + 3x^2 – 40x – 81

=

(x – 5) x (x + 8) - 81
?

undeadknight26 · Answer

The question marks are subtraction signs.