I haven't done this in a while...
I'm attempting to simplify X4-82X2+81 = 0
I took out X3 and reduced it to X3(X-81)(X-1) = 0
If I messed up, I'd appreciate any help. Thanks!
X4-82X2+81 = 0
Alright here we go:
This is called AC, B Method/Factoring middle term.
AC = 81
B = -82
Now we have to find two numbers that give us the product of 81 and sum of -82 and the 2 numbers are (-81; -1).
Now we will substitute the middle term with those two factors there so we will have:
x^4 -81x^2 -1x^2 +81 =0 >> Now we factorize
x^2(x^2-81)-1(x^2-81) =0
(x^2 - 1)(x^2 - 81)=0
Hope it helps.
I hope you see now that you cannot "take out x3" because there is no x3 in "82x2" or "81".I haven't done this in a while...
I'm attempting to simplify X4-82X2+81 = 0
I took out X3 and reduced it to X3(X-81)(X-1) = 0
If I messed up, I'd appreciate any help. Thanks!
The answer above is not complete.
x2 - 1 can be factored further down to (x + 1)(x - 1), and
x2 - 81 can be factored further down to (x + 9)(x - 9)
Then we have,
x4 - 82x2 + 81 = (x2 - 1)(x2 - 81) = (x + 1)(x - 1)(x + 9)(x - 9)