Question

find the value of a if x-a is a factor of the polynomial p(x) =x^3-(a^2-1) x+2​

Answer 1

       

If  (x - a)  is a factor of  p(x) = x³ - (a² - 1)x + 2 = 0,  then  p(a) = 0.

$\Rightarrow\ p(a)=a^3-(a^2-1)a+2=0 \\ \\ \Rightarrow\ p(a)=a^3-a^3+a+2=0 \\ \\ \Rightarrow\ p(a)=a+2=0 \\ \\ \\ a+2=0 \ \ \ \ \ \Longrightarrow\ \ \ \ \ a=\bold{-2}$

Thank you. :-))