Question

Rewrite (6x3 + 9x2 + 7)/(2x3 + 3x2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.

Answer 1

Given:

There is an expression given as below

$\frac{6x^3+9x^2+7}{2x^3+3x^2}$

Required:

We need to convert the given expression in form of q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.

Explanation:

Simplify the given equation

$\frac{6x^3+9x^2+7}{2x^3+3x^2}=\frac{6x^3+9x^2}{2x^3+3x^2}+\frac{7}{2x^3+3x^2}$

Simplify as

Final answer:

$3+\frac{7}{2x^{3}+3x^{2}}$