Question

how do i factor 4x^2+9?

Answer 1

4x² - 9 = (2x - 3)(2x + 3)

Answer 2

April have you been working with complex (imaginary) numbers in your class?

Answer 3

no

Answer 4

and I need the steps of how to get (2x-3)(2x+3)

Answer 5

No? Hmm, did you put a plus when you meant to put a minus? As Haiqa posted.

Answer 6

no

Answer 7

Then its

Answer 8

(2x + 3) ^2

Answer 9

\[\large 4x^2+9\]Does NOT factor into \(\large (2x-3)(2x+3)\) because of the addition betwee the terms. :\

Answer 10

It factors into \(\large (2x-3i)(2x+3i)\)
You sure it wasn't suppose to be subtraction? D: lol

Answer 11

positive lol

Answer 12

Ok well anyway, here is a step that will help.
We want to rewrite each term as a square.

\[\large 4x^2+9 \qquad = \qquad 2^2x^2+3^2 \qquad = \qquad (2x)^2+3^2\]Understand what I did so far?

Answer 13

yes

Answer 14

Since we have the `sum of squares` we can rewrite them as the product of complex conjugates using this rule,\[\large a^2+b^2=(a+bi)(a-bi)\]

Answer 15

l

Answer 16

ok

Answer 17

If you haven't been introduced to imaginary numbers yet, then your book or teacher might actually want you to put "no solution" or something for the answer.
But this is the method we want to use if we're understanding the concept :)

Answer 18

oh wait yeah we did learn about imaginary numbers,

Answer 19

lol :3

Answer 20

(2x-3i)(2x+3i)

Answer 21

Understand how that rule will help us?
In our case we have \(\large a=(2x)\) and \(\large b=3\)

Answer 22

yeah

Answer 23

so would my final answer be (2x-3i)(2x+3i)?

Answer 24

yes :)

Answer 25

do you know WHY it's i though?..

Answer 26

Thanks so much!!!!!!!!!!!!!!!!!!

Answer 27

yeah imaginary number