Question

Which of the following are factors of x^4 − 81? Select all that apply.

Answer 1

Answer:

The factors are

$\text{A. } x^2 + 9$

$\text{D. } x + 3$

Step-by-step explanation:

$x^4- 81$

$(x^2)^2-9^2$

Once $x^2-y^2=\left(x+y\right)\left(x-y\right)$

$\left(x^2\right)^2-9^2 = \left(x^2+9\right)\left(x^2-9\right)$

Now we can factor $x^2-9$ again using difference of two squares:

Therefore,

$\left(x^2+9\right)\left(x+3\right)\left(x-3\right)$

The factors are

$\text{A. } x^2 + 9$

$\text{D. } x + 3$

Answer 2

Answer:

A and D

Step-by-step explanation: