use the factor theorem to show that x-1 is a factor of

Question

use the factor theorem to show that x-1 is a factor of 

P(x)=x³-7x²+14x-8

 

The function value of P(1)=

thus, x-1 is a ........ of P(x) (fill in the blank)

Answer 1

By the factor theorem, if P(1)=0, then x-1 is a factor.

 

P(1)=(1)³-7(1)²+14(1)-8

 

      =1-7+14-8

 

      =-6+14-8

 

      =8-8

 

      =0

 

therefore, x-1 is a factor of P(x).