Question

Rewrite (4x4 + 8x2 + 3)/(4x2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.

Answer 1

(x² + 2) + 3/4x²

Step-by-step explanation

Since the divisor is a single-term polynomial, to write the answer in the requested form, we can distribute the divisor into each of the terms of the dividend,

`(4x^4+8x^2+3)/(4x^2)=(4x^4)/(4x^2)+(8x^2)/(4x^2)+(3)/(4x^2)`

And simplify,

`(4x^4)/(4x^2)+(8x^2)/(4x^2)+(3)/(4x^2)=(x^2^{}+2)^{}+(3)/(4x^2)`

Hence, the answer is (x² + 2) + 3/4x².