Question

factorisation of x4+6x2+25​

Answer 1

Answer:

well, if you add 4x² and substract 4x² you will have:

x^4+10x²+25-4x²

Now you can factor this as:

(x²+5)(x²+5)-4x 2

This is a difference of square:

(x²+5)²-(2x)²

Remember a²-b²=(a+b)(a-b)

(x²+5+2x)(x²+5-2x)

Or equivalently,

(x²+2x+5)(x²-2x+5)

If this were equal to zero, then you could use the quadratic formula on each part to come up with the roots:

x=1+2i

x=1-2i

x=-1+2i

x=-1-2i.