Thread: Questions about factoring an equation with 3rd degree and 2nd degree

This is the equation that needs to be fully factored. So, from what I see here it would be impossible to factor it normally, since 1 can't be multiplied by 3 or any other number to get 1 other then 1.

I figure this is a good idea to use factor theorem. I figured out that p(-1) =0 that would mean that x+1 is a factor of this equation.

next I did division






I got stuck half way through the division when I reached the (x^2 -1)(x^2-x) I don't think i can subtract 1-x. Not sure where to go from here. any help appreciated.

"I figured out that p(-1) = 0 that would mean that x+1 is a factor of this equation." Good, so you have: .
I don't understand what you did in that picture, but from here, in general can be factored: .

~ , for the second bracket x is common factor.

Originally Posted by sara213

This is the equation that needs to be fully factored. So, from what I see here it would be impossible to factor it normally, since 1 can't be multiplied by 3 or any other number to get 1 other then 1.

I figure this is a good idea to use factor theorem. I figured out that p(-1) =0 that would mean that x+1 is a factor of this equation.

next I did division






I got stuck half way through the division when I reached the (x^2 -1)(x^2-x) I don't think i can subtract 1-x. Not sure where to go from here. any help appreciated.

Your idea is sound but you need to remember to include all powers of x when you do division

To clarify you started with

Originally Posted by TheEmptySet

Your idea is sound but you need to remember to include all powers of x when you do division

To clarify you started with

Sorry about the picture...I tired to post it form math type into here and it became huge so I did a gif but that didn't work out well. I wanted to show the division in full process but I couldn't figure out how to add the spaces.

Your right...I forgot about adding the 0x...thank you though. I kind of feel stupid now..lol

Originally Posted by sara213

This is the equation that needs to be fully factored. So, from what I see here it would be impossible to factor it normally, since 1 can't be multiplied by 3 or any other number to get 1 other then 1.

I figure this is a good idea to use factor theorem. I figured out that p(-1) =0 that would mean that x+1 is a factor of this equation.

next I did division






I got stuck half way through the division when I reached the (x^2 -1)(x^2-x) I don't think i can subtract 1-x. Not sure where to go from here. any help appreciated.

Besides long division you can do this by simple "eye", meaning: just complete the second factor to what you need:

...how did I find the factor ? Well, we need , so we must

multiply . After this we need , and we already have , so we have so

far only , so we need to add ...and etc.

Of course, after this we can continue and etc.

Tonio