Question

Which of the following is a factor of 2x^4 + 1 + 3 x^2 ?

A 1 + 2x^2

B 4+x^2

C 2x^2 -1

D 3+x^2

Answer 1

2x^4+1+3x^2=2x^4+3x^2+1
2x^4+2x^2+x^2+1
2x^2(x^2+1)+x^2+1=2x^2(x^2+1)+(x^2+1)
(x^2+1)(2x^2+1)
the factors are (x^2+1),(2x^2+1)
so only option A is right