What is the quotient of (x^3+3x^2-4x-12)/(x^2+5x+8)

Step-by-step explanation:

First, we need to write the polynomial in descending order

Then, grab the term with the highest  power from the polynomial and divide it by the term with highest power from the polynomial located at the other side of the division symbol (this polynomial would be x^2+5x+8)

The result (x^3 / x^2) = x

This term will be part of the solution, and will be use to start the process of division.

This process start with the previous obtained term (x), which will be multiplied by the polynomial from the other side of the division symbol (x^2+5x+8).

The result another is another polynomial

This new polynomial will be multiply by negative 1

The new polynomial is then added to the poly (x^3+3x^2-4x-12)

The result will constitute a new poly, that will be use as the remaining of the division.

Since, our reamining differs from zero, and we still have member to simplify, we repeat the step 1 using the remaining as the new poly that needs to be divided by (x^2+5x+8).

The attached picture explains the whole procedure.

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step-by-step explanation: