The graph with equation y= x^3 - 6x^2 + 11x - 6 intersects the x axis at 1, find the other 2 points at which the graph intersects the x axis

the equation: x³ - 6x² + 11x -6

Becasuse it intersects at the x axis, y=0 so we set the equation equal to 0. x³ - 6x² + 11x -6 =0

we know it intersects the x axis at 1 and so (x-1) is a factor of that equation. so it becomes         (x-1)*(Ax² +Bx +C) where A,B,C are intergers to be found.

we divide (x-1) from the orginal equation             x³ - 6x² + 11x -6.

x³ - 6x² + 11x -6/(x-1) = x²-5x+6

This means we can write the orignal equation    x³ - 6x² + 11x -6 = (x-1)*(x²-5x+6)

we factorise the quadractic equation x²-5x+6. This will become (x-2)(x-3)

Therefore X=2 and X=3, therfore the other two points of intersection are 2 and 3.