Question

Check whether X-2 is a factor of xcube-4xsquare+x-6 using factor theorem​

Answer 1

Step-by-step explanation:

P(x) = $x^{3} - 4x^{2} + x - 6$

P(x - 2) = (x - 2)³ - 4(x - 2)² + (x - 2) - 6

           =  $x^{3} - 8 - 6x^{2} + 12x$ - $4x^{2} + 16x - 16$ + $x - 2 - 6$

           = $x^{3} - 10x^{2} - 29x - 32$

∵ In factor theorem P(x) = 0 here, P(x - 2) ≠ 0

So, (x - 2) is not a factor of $x^{3} - 4x^{2} + x - 6$.