Question

Simplify:

(x^3-8)

ok i know it simplifies to (x-2)(x^2+2x+4)

but i don't know why

Answer 1

just memorise it lol

Answer 2

you can expand to see that its correct,

Answer 3

factors?
okay you know that x=2 is one zero of x^3-8=0
so a factor of x^3-8 is x-2
we can use x-2 to find the other factor(s)
2| 1 0 0 -8
| 2 4 8
_________________________
1 2 4 | 0
so another factor is 1x^2+2x+4

Answer 4

but things like that u just have to memorise

Answer 5

:|

Answer 6

It's the difference of cubes. And no, don't memorize it. Not really worth wasting brain space on. Just know that there is a formula for it, know what it's called, and how to identify it. Then you can look up the formula when you need to. Or you can (as myininaya did) use synthetic division.

Answer 7

where myininaya's post?

Answer 8

i cant remember the formula for factoring difference and sum of cubes
so i always find one zero if f(x)=0 then use it to find the other factor(s)

Answer 9

i know how they get the first bracket but not the 2nd

Answer 10

do you know snytheic of long divison?

Answer 11

why not memorise lols , its just like the difference of sqaures formula.

some people dont know polynomial division ( I know in high schools in Australia you dont get taught polynomial division if you are in the basic calculus subject ) and even if you do its not worth the time manually doing it

Answer 12

or*

Answer 13

i like to know how formulas are derived

Answer 14

a^3-b^3 = (a-b)(a^2 +ab +b^2)

easy as to remember

Answer 15

a^3-b^3 = (a-b)(a^2 +ab +b^2)

easy as to remember

Answer 16

yes myininaya i know how to do synthetic division i just saw your post sorry

Answer 17

lol
but more fun to divide! :)

Answer 18

divide and conquer!

Answer 19

then for the sum of cubes you change the a-b to a+b , and you swap the sign on ab

Answer 20

lol i see what your sayin elecenginer

Answer 21

you always know the signs in first bracket ( because they come from whether its sum or difference ) , then u make sure u have different sign on the ab term

Answer 22

i remember the basic form i just have to do it to remember where to put the plus and minus (i always have to find one zero to help me set the factors up

Answer 23

lol ok thanks so much guys

Answer 24

np