Question

Which choice is a factor of x^4-1 when it is factored completely?

a.) x^2-1
b.) x-1
c.)x
d.)1

Answer 1

Remember how to factor the difference of SQUARES? c:
\[\large a^2-b^2=(a-b)(a+b)\]
We can manipulate this thing to make it look like the difference of squares.

Answer 2

^-^ mmhmm

Answer 3

\[\large x^4-1\qquad\rightarrow\qquad x^4-1^4 \qquad\rightarrow\qquad (x^2)^2-(1^2)^2\]Now we have the difference of squares.
Applying the rule gives us,\[\large \left(x^2-1^2\right)\left(x^2+1^2\right)\]

Answer 4

Now the problem has some tricky little wording :)
You might look at your factors and go "AHA! I see \(x^2-1\)!"

But the instructions ask you for a factor after you've COMPLETELY factored it.
We can actually factor this a bit further.

Answer 5

because \(x^2-1^2\) is also the difference of squares! Let's apply the rule again.

Answer 6

\[\large \color{orangered}{\left(x^2-1^2\right)}\left(x^2+1^2\right)\qquad\rightarrow\qquad \color{orangered}{(x-1)(x+1)}\left(x^2+1\right)\]

Answer 7

NOW it's finally fully factored :D Do any of those factors match your choices?

If you're confused by any step, let me know :U

Answer 8

B?

Answer 9

ya

Answer 10

So its B :o