1. Polynomials

Im supposed to factor polynomials but I have three problems I cant figure out
( when I have ^, it means its an exponent

Thanks for any help I can get

#1 12m^2 - m - 6
Im not sure what to do with the 12

#2 x^4 - 81

Im supposed to simplify
#3 x^2 over (x^2 - x)(x-1)^-1

Thanks Again

2. Originally Posted by wpcp15
Im supposed to factor polynomials but I have three problems I cant figure out
( when I have ^, it means its an exponent
Thanks for any help I can get

#1 12m^2 - m - 6
Im not sure what to do with the 12
#2 x^4 - 81
Im supposed to simplify
#3 x^2 over (x^2 - x)(x-1)^-1
Thanks Again
Hello, wpcp,

to 1.: You can put the 12 before paranthese and afterwards factor the contents of the bracket as usual:
$\displaystyle 12m^2 - m - 6=12 \cdot \left(m^2-\frac{1}{12}m-\frac{1}{2}\right) =12 \left(m+\frac{2}{3}\right) \left(m-\frac{3}{4}\right)$

to 2.: Remember that x^4 = (x^2)^2 and of course 81 = 9^2. So you've got a binomial formula:
$\displaystyle x^4-81=\left(x^2\right)^2-9^2=(x^2+9)(x^2-9)$

to 3.: Rewrite this term:

$\displaystyle \frac{x^2}{(x^2 - x)(x-1)^{-1}}=\frac{x^2}{(x^2 - x)\cdot \frac{1}{x-1}} = \frac{x^2 \cdot (x-1)}{x(x-1)} = x,\ \ x\neq 0\ \wedge \ x\neq1$

EB