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

ANSWER

(x² + 2) + 3/4x²

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,

$\frac{4x^4+8x^2+3}{4x^2}=\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}$

And simplify,

$\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}=(x^2^{}+2)^{}+\frac{3}{4x^2}$

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