Mathematico | Mathematico

The cubic

y = (x + 1) (x^{2} + 3 x - 17)

intersects with the line

y = x + 1

at three distinct points. Find the coordinates of these three points.

To find the $x$ coordinates of the points of intersection, you would need to solve

(x + 1) (x^{2} + 3 x - 17) = x + 1

Again, don't expand the brackets: you can remove a common factor of $x + 1.$

You can use a similar idea to what we used in the previous problem:

\underset{⏟}{(x + 1)} (x^{2} + 3 x - 17) - \underset{⏟}{(x + 1)}