Question

Factor completely X⁴-10x²+9. Please show all work.​

Answer 1

Let y=x² . Then:

x4−10x2+9=y2−10y+9

y²-10y+9=(y-9)(y-1)

Substitute x² for y:

x4−10x2+9=(x2−9)(x2−1)

x²-9=(x+3)(x-3)

x²-1=(x+1)(x-1)

x4−10x2+9=(x+3)(x−3)(x+1)(x−1)