Question

x的4次方+x²+1 因式分解，我悬赏50分

x³-3x²+4，a²+ax-2a-x+1 ，4x的4次方+a的4次方 都是因式分解

Answer 1

x⁴+x²+1
=x⁴+2x²+1-x²
=(x²+1)²-x²
=(x²+x+1)(x²-x+1)

x³-3x²+4
=x³-3x²+2x-2x+4
=x(x-1)(x-2)-2(x-2)
=(x-2)(x²-x-2)
=(x-2)(x-2)(x+1)
=(x-2)²(x+1)

a²+ax-2a-x+1
=a²-2a+1+x(a-1)
=(a-1)²+x(a-1)
=(a-1)(x+a-1)

4x⁴+a⁴
=4x⁴+4x²a²+a⁴-4x²a²
=(2x²+a²)²-(2ax)²
=(2x²+2ax+a²)(2x²-2ax+a²)