Question

Rewrite the expression (19x3 – 5x2 + 6x – 2)/(x + 1) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor, using the long division method.

Answer 1

We are asked to perform the long division on the following expression.

$\frac{(19x^3-5x^2+6x-2)}{(x+1)}$

Let us perform the long division.

So, we have

Quotient: q(x) = 19x^2 - 24x + 30

Remainder: r(x) = -32

Divisor: b(x) = x + 1

Therefore, the equivalent expression is

$19x^2-24x+30-\frac{32}{(x+1)}$

The 3rd option is the correct answer.