Question

URGENT

Divide f(x) by d(x), and write a summary statement in the form indicated.

f(x) = x4 + 4x3 + 6x2 + 4x + 5; d(x) = x2 + 1

answer choices:
f(x) = (x2 + 1)( x2 + 4x + 5) + 12x - 15
f(x) = (x2 + 1)( x2 + 4x + 5)
f(x) = (x2 + 1)( x2 - 4x + 5)
f(x) = (x2 + 1)( x2 - 4x + 5) + 12x - 15

Answer 1

The answer to your question is: (x² + 4x + 5)(x² + 1) Second option

Explanation:

x² + 4x + 5

x² + 1 x⁴ + 4x³ + 6x² + 4x + 5

-x⁴ - x²

0 + 4x³ + 5x² + 4x

- 4x³ -4x

0 +5x² 0 + 5

-5x² -5

0 0

Remainder = 0

The first and the last options are not solutions because there was not remainder.

The third option is incorrect because the second term is negative and must be positive.