Question

Write as a product of linear factors: f(x)= x^4 -100 ??

Answer 1

start by factoring the difference of two squares
\[x^4-100=(x^2+10)(x^2-10)\]

Answer 2

then for the second part repeat to get
\[(x^2+10)(x+\sqrt{10})(x-\sqrt{10})\]

Answer 3

if you need linear factors you need complex numbers because the first part does not factor over the integers.
you would get
\[(x+\sqrt{10}i)(x-\sqrt{10}i)(x+\sqrt{10})(x-\sqrt{10})\]

Answer 4

thank you!

Answer 5

yw