Question

Need help using synthetic division! ​

Answer 1

Answer:

$3x^{2} -3x+8-\frac{9}{x+1}$

Step-by-step explanation:

Since we're dividing the polynomial by $(x+1)$, we'll be using -1 to start the division.

Before setting the division up, let's list the coefficients of $x$ from descending powers and the constant.

The coefficient of $x^{3}$ is 3

Since we don't see an $x^{2}$, the coefficient will be 0.

The coefficient of $x$ is 5.

Lastly, the constant, which is the term without the $x$ is -1.

Refer to the attached picture before continuing.

After referring to the picture, we now have the coefficients for the quotient.

The coefficient of $x^{2}$ is 3.

The coefficient of $x$ is -3.

The constant is 8.

Lastly, since the last number is not zero, it's the remainder just like regular division. This can be tricky to remember, but -9 is not the actual remainder.

The remainder is actually $\frac{-9}{x+1}$.

Now putting all the pieces together, we get:

$3x^{2} -3x+8-\frac{9}{x+1}$