Question

$x {2} - 2x {2} - x + 2 \: factorise$
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Answer 1

Step-by-step explanation:

This is not factorable normally. We can see this since #x^2-2x+1# is a perfect square, so it touches the x-axis at a single root. Adding 1 to this produces #x^2-2x+2#, and raises the graph of #y = x^2-2x+1# one upwards, meaning it no longer touches the x-axis, so it has no real roots.

Answer 2

Step-by-step explanation:

x^2-2x^2-x+2

=-x^2-x+2

=-x^2-2x+x+2

=-x (x+2)+1 (x+2)

=(x+2)(-x+1)