Question

Write a linear factorization of the function.

f(x) = x^4 + 64x^2

Answer 1

f(x) = (x)(x)(x^2 + 64)
f(x) = (x)(x)(x+8i)(x-8i)

Answer 2

can you show me the steps please?

Answer 3

We have
\[f(x)=x^4+64x^2\]
first step is to take x^2 common from both the terms, we get
\[f(x)=x^2(x^2+64)\]
Do you get this @madixy ?

Answer 4

yes! :)

Answer 5

Have you studied complex no.s ?

Answer 6

yes but I still have trouble with "i"

Answer 7

basically, think of it as a difference of squares:
x^2+64 = x^2-(-8)^2

Answer 8

^ + -8^2

Answer 9

we know that
\[\sqrt{-1} =i\]
I'd rewrite f(x) as
\[f(x)=x^2(x^2-(-64))\]
do you get this point?

Answer 10

yes i get it now! thank you!

Answer 11

could you solve the rest?

Answer 12

x^2(x + 8i)(x - 8i)

Answer 13

Good work:D

Answer 14

thanks again!