Question

What is the completely factored form of t4 − 16?

Answer 1

ok did u try it?

Answer 2

Yes. I got (t2-4)(t2+4)

Answer 3

Thats correct :)

Answer 4

ok thanks:)

Answer 5

Wait! No it's not. I got it wrong:(

Answer 6

(t2+4)(t+2)(t−2)

Answer 7

i was thinking both of them are the same thing

Answer 8

Ohhh okay :)

Answer 9

what was the right answer?

Answer 10

Yes:)

Answer 11

:)
welcome to openstudy :)

Answer 12

haha thanks :)

Answer 13

Factoring means factoring completely.
When you have to factor a polynomial of two terms, look for the difference of squares or the sum or difference of cubes.
The first step in factoring, though, is always to look for a common factor.
In this case there is no common factor.
Then you have two terms.
t^4 is obviously not a cube, so look at the difference of two squares.
Sure enough, \(t^4 - 16\) can be written as \( (t^2) - 4^2 \) which clearly looks like the difference of two squares.

Answer 14

The difference of squares factors like this:

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

Your expression factors similarly:

\((t^2)^2 - 4^2 = (t^2 + 4)(t^2 - 4) \)

Now you need to look at each factor to see if it can be factored further.

\(t^2 + 4\) is a sum of squares. It can't be factored.
Now we look at \(t^2 - 4\) which is a difference of squares and can be factored.

\(t^4 - 16 = (t^2)^2 - 4^2 = (t^2 + 4)(t^2 - 4) = (t^2 + 4)(t + 2)(t - 2) \)

Finally we look at the new factors, t + 2 and t - 2, and we see that they can;t be factored any further, so our answer above is fully factored.