Question

I don't know how to solve.. please show work
3x^3 +7x^2 +x -2

Answer 1

This is a cubic form. I am assuming this should be factored.

With cubics like this it's worthwhile trying to find one root by simply guessing. My guess that worked out is x=-2

To verify:

3(-2)^3+7(-2)^2+(-2)-2 = 0 -> so -2 is a root and we get the first factor: (x+2)

Next we divide the cubic by the factor (x+2). I let you do the division. Here is the result

(3x^3 +7x^2 +x -2):(x+2) = (3 x^2 + x - 1)

(3 x^2 + x - 1) is a quadratic form and you can use the quadratic formula to get the two other roots. I got
`(-1\pm √(13))/(6)`.

So the entire cubic is now factored as follows:

`(x+2) \cdot (x+ (-1+ √(13))/(6)) \cdot (x+ (-1- √(13))/(6))`

Answer 2

3x^3+7x^2+x-2
= (x+2) x (3x^2+x-1)