Question

Which of the following is a factor of x^4 - 8x^2 + 16?

a) x^3
b) x^2 - 4
c) x - 4
d) x + 4

Answer 1

The factor of x^4 - 8x^2 + 16 is x + 4.

Step-by-step explanation:

The given expression is x^4 - 8x^2 + 16.

Let's check which of the given options is a factor of this expression:

1. (a) x^3: To see if it's a factor, we can divide x^4 - 8x^2 + 16 by x^3. We get x - 8 + (16/x), which means x^3 is not a factor.
2. (b) x^2 - 4: Again, we divide x^4 - 8x^2 + 16 by x^2 - 4. We get x^2 + 4 + (16/x^2), so x^2 - 4 is not a factor either.
3. (c) x - 4: Dividing x^4 - 8x^2 + 16 by x - 4 gives us x^3 + 4x^2 - 16x - 64 + (256/x - 16/x^2), indicating that x - 4 is not a factor.
4. (d) x + 4: Finally, dividing x^4 - 8x^2 + 16 by x + 4 yields x^3 -4x^2 - 16x + 64 + (0/x), which means x + 4 is a factor of the expression.

Therefore, option d) x + 4 is a factor of x^4 - 8x^2 + 16.