algebra factor touble with derivative

[delgeezee]

I am practicing with one of the example is the book. But i am having trouble with the factoring part. I have to find the derivative of
\(\displaystyle f=3x^4-4x^3-6x^2+12x+1\)
i get to

\(\displaystyle f'=12x^3-12x^2-12x+12\)

\(\displaystyle f'=12(x^3-x^2-x+1)\)

how do I factor\(\displaystyle (x^3-x^2-x+1) \) ???

 

[lookagain]

\(\displaystyle How \ do \ I \ factor \ (x^3 - x^2 - x + 1)?\)

Factor by grouping occurs to me, and you can group them in different ways to factor:


\(\displaystyle A) \)


\(\displaystyle (x^3 - x^2) - (x - 1)\)

\(\displaystyle x^2(x - 1) - 1(x - 1)\)

\(\displaystyle (x - 1)(x^2 - 1)\)

\(\displaystyle (x - 1)(x - 1)(x + 1)\)

\(\displaystyle (x + 1)(x - 1)^2\)


----------------------------------------------


\(\displaystyle B)\)


\(\displaystyle x^3 - x - x^2 + 1\)

\(\displaystyle x(x^2 - 1) - 1(x^2 - 1)\)

\(\displaystyle (x^2 - 1)(x - 1)\)

\(\displaystyle (x - 1)(x + 1)(x - 1)\)

\(\displaystyle (x + 1)(x - 1)^2\)


---------------------------------------------


\(\displaystyle C)\)


\(\displaystyle x^3 + 1 - x^2 - x\)

\(\displaystyle (x^3 + 1) - 1(x^2 + x)\)

\(\displaystyle (x + 1)(x^2 - x + 1) - x(x + 1)\)

\(\displaystyle (x + 1)(x^2 - x + 1 - x)\)

\(\displaystyle (x + 1)(x^2 - 2x + 1)\)

\(\displaystyle (x + 1)(x - 1)(x - 1)\)

\(\displaystyle (x + 1)(x - 1)^2\)

 

[tkhunny]

It is a sad state of affairs that you managed to get to calculus without the Rational Root Theorem.

See all those '1's in there? Try (x-1) and (x+1).

Please read up on some algebra that you seem to be missing. You will struggle beyond your ability to enjoy the calculus if you don't get your algebra up to speed.