Question

Show that( x-1)( x-2) is a factor of x^3-x^2-4x+4

Answer 1

Answer: Let x-1 be g(x)

And Let x-2 be f(x)

g(x): x-1=0

x=1

p(x)=x^3-x^2-4x+4

p(1)= (1)^3-(1)^2-4(1)+4

= 1-1-4+4

= 0

therefore, g (x) is a factor of p(x)

Now, f(x): x-2=0

x=2

p(x)=x^3-x^2-4x+4

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

= 8-4-8+4

= 0

Therefore, f(x) is also a factor of p(x)

I hope this will help you