Question

Check whether , x - 2 is a factor of the polynomial x3 - x2 - 4 by using factor theorem.

Answer 1

Let,
x-2=0

x=2

Substitute value of x in the above equation

=(2)^3-(2)^2-4

=8-4-4

=0

Answer 2

Explanation :

Factor theorem

If x - a is a factor of a function f ( x ) then x = a is a solution or zero of the function given .

Checking whether it holds true for f ( x )

x - 2 = 0

= > x = 2

Put this in f ( x )

x³ - x² - 4

= > 2³ - 2² - 4

= > 8 - 4 - 4

= > 8 - 8

= > 0

Hence f ( x ) = 0

This proves that x - 2 is a factor !

Hope it helps !

______________________________________________________