1. ## cubic help

we were given a function of y=(x-a)(x-b)(x-c) and were told to add in our own numbers i chose y=(x-8)(x+5)(x-3). can some one show me the working to get it to a cubic and then the derivative

2. Originally Posted by psychosocial for life
we were given a function of y=(x-a)(x-b)(x-c) and were told to add in our own numbers i chose y=(x-8)(x+5)(x-3). can some one show me the working to get it to a cubic and then the derivative
lets say it was (x - 8)(x + 5), could you expand that?

expand the first two first, and then multiply what you got by the (x - 3). how? first multiply everything by the x and then multiply everything by the -3

when finding the derivative, all that is needed is the power rule: $\frac d{dx} x^n = nx^{n - 1}$

and of course, if there are constants in front of the x's, you just leave them and multiply what you got by them since $\frac d{dx}[c f(x)] = c \frac d{dx}f(x)$. here, your $f(x)$ is $x^n$

(why did you choose such big numbers? )

3. thanks for the help
(why did you choose such big numbers? )
Dont know but regreting it now

4. Originally Posted by psychosocial for life
thanks for the help

Dont know but regreting it now
okie dokie.

5. for some reason it still isnt working out right could you please show me the working out so i can workout what im doing wrong. i just cant work it out

6. Originally Posted by psychosocial for life
for some reason it still isnt working out right could you please show me the working out so i can workout what im doing wrong. i just cant work it out
$\underbrace{(x - a)(x - b)}_{\text{do these two first}}(x - c) = [x^2 - (a + b)x + ab](x - c)$

now we take the x in the second set of brackets and multiply everything in the first set, after that, we take the -c in the second set of brackets and multiply everything in the first set. so we get:

$\underbrace{x^3 - (a + b)x^2 + abx}_{\text{everything in the first set times }x}~~~ \underbrace{- cx^2 + c(a + b)x - abc}_{\text{everything in the first set times }-c}$

now group the like terms and simplify

$x^3 - (a + b + c)x^2 + (ab + ac + bc)x - abc$

7. thank you again i found out what i did wrong. i got x^3-6x^2-31x-120

8. Originally Posted by psychosocial for life
thank you again i found out what i did wrong. i got x^3-6x^2-31x-120
it should be + 120

9. sorry miss type i got +120