Question

Can someone help me with this?

Answer 1

http://prntscr.com/dgpuqy

Answer 2

first factor over the real numbers
do you recognize it as a perfect square?

Answer 3

I'm not really good with the technical terminology

Answer 4

a perfect square means some expression squared, like \[(2+x)^2\]

Answer 5

it is always the case that \[(a+b)^2=a^2+2ab+b^2\]
you have something that looks very much like \[a^2+2ab+b^2\]in your expression \[x^2+10x^2+25\]

Answer 6

oops i meant in \[x^4+10x^2+25\]

Answer 7

idk the teacher always told me to start by finding the GCF

Answer 8

so it's \[(x+5)^{2}\] ?

Answer 9

close
it is \[(x^2+5)^2\]

Answer 10

is that because of the x^4?

Answer 11

right

Answer 12

so now you are done factoring with real numbers
for complex numbers, do you know how to solve \[x^2+5=0\]?

Answer 13

you take the square root of them?

Answer 14

first, subtract \(5\) from both sides

Answer 15

okay

Answer 16

then take the square root
don't forget the \(\pm\)

Answer 17

\[x=i \pm \sqrt{5}\]

Answer 18

like that?

Answer 19

no not quite

Answer 20

\[x^2=-5\\
x=\pm\sqrt{-5}\\
x=\pm\sqrt{5}i\]

Answer 21

the i is separate from 5 right?

Answer 22

yes, outside, not under the radical

Answer 23

now that you have the zeros, you factor \[x^2+5=(x+\sqrt5 i)(x-\sqrt5 i)\]

Answer 24

omg thanks so much :)

Answer 25

yw, don't forget to write your final answer

Answer 26

\[\left\{ x+\sqrt{5}i , x-\sqrt{5}i \right\}\]