Question

Factor the polynomial function over the complex numbers.

Can someone please check my work I don’t think I did it right thank you

Answer 1

Explanation:

f(x)=x^4+3x^2-4

put x²=y

squaring x^4=y²

f(x)=y²+3y-4

=y²+4y-y-4

=y(y+4)-1(y+4)

=(y+4)(y-1)

so f(x)=(x²+4)(x²-1)

=[x²-(-4)](x²-1²)

=[x²-(4i²)](x²-1²)

=[x²-(2i)²](x²-1²)

=(x+2i)(x-2i)(x+1)(x-1)

[∵a²-b²=(a+b)(a-b)]