how to factor x4 - 1?

Answer 1

(x² - 1)(x² + 1)
(x - 1)(x + 1)(x² + 1)

Answer 2

Factor X 4

Answer 3

(x^2 +1)(x^2 - 1)

Answer 4

x^4-1 =(x^2-1)(x^2+1)
=(x+1)(x-1)(x^2+1)

Answer 5

I find that a lot of students factor everyday in math courses without knowing the meaning of factoring.

What does it mean to FACTOR?

Factoring is the REVERSE of multiplication. Factoring is the process of taking what was once a product and breaking it into little original pieces called FACTORS.

Sample: Factor 40.

If you recall, we used something called a factor tree and to BREAK DOWN 40 into little original pieces called FACTORS of 40. Here, 40 is the PRODUCT that you must break down using the factor tree method to find the factors of 40.

The same idea applies to your question.
x^4 - 1 is your product and we must break it down into little ORIGINAL PIECES called FACTORS.

What TWO FACTORS when multiplied will produce x^4 -1?

How about (x^2 -1) and (x^2 + 1)....These are the two factors.

However, this guy (x^2 -1) can be reduced even more.

This guy (x^2 - 1) is called the difference of two perfect squares.

So, what two factors when multiplied give us (x^2 -1)?

How about (x - 1) and (x + 1)???

Put it all together:

(x^4 - 1) becomes (x - 1) (x + 1) (x^2 + 1)....our final answer.

By the way, the factor (x^2 + 1) cannot be reduced anymore because it is already in lowest terms. In other words, you cannot break down the SUM of squares.

Got it?

Answer 6

Assuming you mean x^4 - 1...

Let y = x^2

Then we have y^2 - 1
y^2 - 1 = (y+1)(y-1) = (x^2 + 1)(x^2 - 1) = (x^2 + 1)(x+1)(x-1)

Thus x^4 - 1 = (x^2 + 1)(x+1)(x-1)

Answer 7

x^4-1
(x^2+1)(x^2-1)
(x^2+1)(x-1)(x+1)

Answer 8

This Site Might Help You.

RE:
how to factor x4 - 1?

Answer 9

That's a difference of squares:

(x²)² - 1²

Remember that can be rewritten as (a + b)(a - b)

(x² - 1)(x² + 1)

But the first expression is also a difference of squares, so do it again:

(x - 1)(x + 1)(x² + 1)

There you go (you can't do anything with the sum of squares).

Answer 10

you cant, it is a prime number: 1(x4-1) or 24-1(1)