Question

x - 2 is a factor of x 4 + 3x 3 - 5x 2 + 2x - 24 True False

Answer 1

Using remainder theorem:

g(x) = x-2

=> x-2=0

=> x=2

p(x) = x^4+3x^3-5x^2+2x-24

Substituting the value of x:

p(x)=(2)^4+3(2)^3-5(2)^2+2(2)-24

=> 16+3(8)-5(4)+2(2)-24

=> 16+24-20+4-24

=> 16+24+4-20-24

=> 44-44=0

Hence, as the remainder is 0,

(x-2) is a factor.

Therefore, the statement is true.