Hello,
1) 4x^3-32=0
==>4(x^3-8)=0
==>4(x-2)(x²+2x+4)
==>x=2
2) 64x^3-1=0
==>(4x)^3-1=0
==>(4x-1)(16x^2+4x+1)
==> x=1/4
3)
x^4-5x^2+4=0
==>x^4-x²-4x²+4=0
==>x²(x²-1)-4(x²-1)=0
==>(x²-1)(x²-4)=0
==>(x-1)(x+1)(x-2)(x+2)=0
==> x=1 or x=-1 or x=2 or x=2
4)
x^4-10x²+16=0
==>x^4-2x²-8x²+16=0
==>x²(x²-2)-8(x²-2)=0
==>(x²-2)(x²-8)=0
==>(x-√2)(x+√2)(x-2√2)(x+2√2)=0
==>x=√2 or x=-√2 or x=2√2 or x=-2√2
5)
x^4-9x²+14=0
==>x^4-7x²-2x²+14=0
==>x²(x²-7)-2(x²-7)=0
==>(x²-7)(x²-2)=0
==>(x-√7)(x+√7)(x-√2)(x+√2)=0
==>x=√7 or x=-√7 or x=√2 or x=-√2