Question

use factor theorem to show that (x+2)(x+1) is a factor of polynomial p (x)=x^4+x^3+2x^2+4x-8

Answer 1

By using factor theorem,

if the( x+2) are the factor of the polynomial then ,

X+2=0

X= -2

therefore

p(x)= X^4+X^3+2x^2+ 4x-8

X = -2 taking

p(-2) = (-2)^4+(-2)^3+2(-2)^2+4(-2)-8

= 16+(-8)+2(4)-8-8

= 16+(-8)+8-8-8

= 8+8-8-8

=16-8-8

= 8-8

= 0
Therefore (X+2) are the factor of the given polynomial.

Similarly you can solve another one.