Thread: factorise

hi, i need to factorise this, x^2-121.
would i do this, x(x-121)??

Originally Posted by andyboy179

hi, i need to factorise this, x^2-121.
would i do this, x(x-121)??

Hint: $\displaystyle 121=11^2$. The recall the factoring formula for the difference of squares $\displaystyle x^2-a^2$.

Can you proceed?

ok, qwould it be x(x-11^2)??

Originally Posted by andyboy179

ok, qwould it be x(x-11^2)??

Not really. You can't factor out the x like that. What you have would be correct if the original problem was to factor $\displaystyle x^2-121x$.

But what you have here is $\displaystyle x^2-121 = x^2-11^2$. So you need to use the difference of squares formula $\displaystyle x^2-a^2=(x+a)(x-a)$.

Can you proceed?

oh yes i see, it would be (x^2 -11^2)?

Originally Posted by andyboy179

oh yes i see, it would be (x^2 -11^2)?

But that's not fully factored! Apply the formula I gave you with $\displaystyle a=11$...

(x-11^2) (x+11^2)???

No. You are guessing!!

$\displaystyle (a)^2-(b)^2=(a+b)(a-b)$

$\displaystyle (x)^2-(11)^2=???$

Originally Posted by andyboy179

(x-11^2) (x+11^2)???

One thing you should learn to do, and this is very, very important: Check your potential answers by expanding them to see if you end up with your original problem. Have you learned the FOIL method? You must have learned how to expand them before getting into factoring.

For example, with that, let's check your last attempt:
$\displaystyle (x - 11^2)(x + 11^2) = x^2 + 11^{2}x - 11^{2}x - 11^4 = x^2 - 11^4$

Oops, not yet correct. Can you tell what you did wrong from the result? That last term was from multiplying the last part of each factor (the 11^2) together. What would need to be multiplied to make 11^2 rather than 11^4?

would this be it?

That is not factoring - thats solving - you need (x+??)(x-??) - don't give up, just try again!
Have a read of this Difference of two squares - Wikipedia, the free encyclopedia

would it be (x+11) (x-11)?

Andyboy179

Well you tell me - what do you get if you expand your result?

x^2 - 11^2 which is x^2 - 121

Hi Again,

No to expand you multiply each part so you get:
(x+11)(x-11)=[x*x][x*-11][11*x][11*-11]=x^2-11x+11x-121=x^2-121
This is what you started with, so yes you have factorised it correctly