I need help with algebra, please read details?

Question

I don't know how to insert powers in the computer so any munber that is between a ` sign means power
OK so I have to factor polynomials, and the book explains it like this:

3k~4~-48
3k`4`-48= 3(k`4`-16)
=3(k`2`-4)(k`2`+4)
=3(k-2)(k+2)(k`2`+4) -Then it reads "k`2`+4 cannot be factored. Why not?

I want to know why, please explain in detail how to get the result of that one problem.

-Thank you

Answer 1

to represent powers you use "^" so X^2 means X squared...

I take it that your equation is 3(K^4)-48...

First you factor out 3 from the equation and get 3(K^4 - 16).. Note that you used to have 3 (K^4) and 3(16)

Then, since K^4 and 16 are both perfect squares then you have the difference of squares.. which means your factors are the sum of the square roots and the difference of the square roots..

or: 3 (K^2 - 4) ( K^2 + 4) and note that K^2 - 4 is also the difference of perfect squares.. so it can also be factored...

3(K - 2) (K+2) (K^2 + 4) but your book is correct, you cannot factor K^2 +4.. try it.. if you try K + 2 then you will end up with a middle term when you multiply.. it takes the "+" and "-" to cancel out that middle term which you don't have in this case....

K + 2
K + 2
-------
K^2 + 4K + 4 and you have an "extra" 4K to deal with.

Answer 2

I will write k squared as k^2

k^2 can't be factored (without using imaginary numbers) because they have no common factors besides 1. If you tried FOIL,
(k+2)(k+2) gives an extra 4k; similarly (k-2)(k-2) gives an extra -4k. And (k+2)(k-2) would end in -4, not +4.

Answer 3

wat does ~ mean