Question

how to completely factor 6x^2 - 54?

Answer 1

??

Answer 2

Nvm that

Answer 3

hold on

Answer 4

oh right i see where i went wrong

Answer 5

to factorise something, look for a factor that you can divide the equation by.

Answer 6

Can you see anything you can divide by?

Answer 7

Do you know how to break 52 into it's prime components?

Answer 8

no

Answer 9

But I can divide 54 by 9 and get 6

Answer 10

You know what a prime number is right? like 2,3,5,7,11, etc.

Answer 11

yes

Answer 12

alright, that is already one part of the step

Answer 13

Prime numbers are like atoms of numbers, you can break every number into little pieces until you can no longer divide them

Answer 14

For example

\[54 = 9*6 = 3*3*3*2\]

Answer 15

There you have it broken down in the smallest way possible. Now if you do this for every number in your equation you can easily see which one you can factor out.

Answer 16

\[\large \color{red} 3\color{red}*\color{red}2*x ^{2}-\color{red}3^{3}*\color{red}2\]

Answer 17

ohh i understand

Answer 18

how do factor it out?

Answer 19

i broken it down as an example, can you see how to factor this?

Answer 20

Do you understand what i did there?

Answer 21

oh the 6 is supposed to be a 3

Answer 22

i'll rewrite it

Answer 23

\[\large \color{blue}3\color{blue}*\color{blue}2*\color{red}x^\color{red}2\color{green}-\color{red}3^\color{red}2*\color{blue}3\color{blue}*\color{blue}2 = \color{blue}3\color{blue}*\color{blue}2\left( \color{red}x^\color{red}2\color{green}-\color{red}3^\color{red}2 \right)\]

Answer 24

sorry that took so long i was trying to make it clear with colors to show you what happens. So do you see what happened there or do you want me to explain in more detail?

Answer 25

@luvsofi are you there?

Answer 26

yes

Answer 27

could you explain further?

Answer 28

sure

Answer 29

so you see, when you calculate an equation, every time there is a + or a - or a = sign, you have to make sure that when you divide by anything, you divide by the same thing after every sign right?

Answer 30

If that makes sense.

Answer 31

for example 5+10=15 i can divide by 5 and it will say 1+2=3 and even though the equation itself is not the same it's still true. and also if i write it like 3*(1+2=3) than solving the brackets will give me the same equation, right?

Answer 32

yes

Answer 33

so the same concept is what i did with the colored equation. the green minus sign is the imaginary line. and we divide by the blue factors which are on both sides of the line and put brackets around everything else

Answer 34

than put the blue factor back outside the brackets to make sure you still have the same thing if you would solve the brackets.

Answer 35

sorry i'm just not understanding, i'll just ask my teacher. thank you anyways!

Answer 36

you can in this case also factorize the factor inside the brackets one more time, by the way. can you see how?

Answer 37

alright, no problem.