firstly, if I want to find the points on intersection on this graph between the curve and line, I'd set thier y values equal to each other.
how do I solve that?
or do I not need these points when working out the area ?
Rational root theorem - Wikipedia, the free encyclopedia
In this case, we can easily see that x=1 is the root we're looking for.
The typical process for finding all roots is to first guess one root using the theorem I linked to above, and then use polynomial long division to factor the polynomial.
For example, if one root is x=1, then you divide the original polynomial with x-1.
And no, your process isn't correct. x=2 and x=-1 aren't roots to the posted polynomial.