Question

GIVING BRAINIEST IF CORRECT!! Factor x^4 - 16 completely

Answer 1

Answer:

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

Step-by-step explanation:

Hello!

We can use the difference of square method.

Difference Of Squares (DOS)

The formula for the DOS is $(a + b)(a - b) = a^2 - b^2$

It is a simple way to factor polynomials.

The criteria:

• Has to begin and end with a perfect square
• The operation has to be subtraction

Factor:

• $x^4 - 16$

Begins with a perfect square (x² * x²) and ends with a perfect square (4 * 4)

• $(x^2 + 4)(x^2 - 4)$

Warning! Watch out, there may be another DOS!

$x^2 - 4$ is another DOS

• $(x^2 + 4)(x + 2)(x - 2)$

The x² + 4 is not a DOS because the operation is addition.

The final factored form is $(x^2 + 4)(x + 2)(x - 2)$