Question

determine the value of (a)if (x-a) is a factor of x^3-(a^2-1)x+2

Answer 1

Answer:

a= -2

Step-by-step explanation:

p(x)= x^3-(a^2 - 1)x + 2=0

if x-a is a factor of p(x), then,

p(a) = 0

therefore, x-a = 0

hence, x=a.

substituting the value of x in p(x), we get,

p(a) = a^3 -(a^2 - 1)a + 2 = 0

= a^3 -(a^3 - a) + 2= 0

= a^3 - a^3 + a + 2=0

=0+a+2=0

therefore, a= -2