Question

Write a linear factorization of the function.

f(x) = x4+ 9x2

f(x) = x2(x + 3i)(x - 3i)

f(x) = x2(x + 3i)2

f(x) = x2(3x + i)(3x - i)

f(x) = x2(3x + i)2

Answer 1

factor gcf first

Answer 2

greatest common facor

Answer 3

?

Answer 4

\(f(x) = x^4+ 9x^2\)
\(= x^2(x^2 + 9)\)

Answer 5

Thats cool didnt know that... whoopsie

Answer 6

its okay, next find the zeroes of \(x^2+9\)

Answer 7

and write the zeroes as factors

Answer 8

x^2 + 9 and x^2 - 9?

Answer 9

\(x^2 + 9 = 0\)

\(x^2 = - 9 \)

\(x = \pm 3i \)

Answer 10

since \(\pm 3i\) are zeroes of \(x^2+9\), \((x+3i)(x-3i)\) are factors of it.

Answer 11

±3 gotcha

Answer 12

dont forget \(i\)

Answer 13

oops

Answer 14

Overall,

\(x^4+ 9x^2 = x^2(x+3i)(x-3i)\)