Question

I am unsure of how to approach this equation. We are tasked with solving it using either Long Division or Synthetic Division.

Answer 1

1st step : Arrange the exponent of x of the dividend from highest to smallest.

Note that you need to add a term in between with 0 as coefficient.

$2x^3+2\Rightarrow2x^3+0x^2+0x+2$

2nd step is to equate the divisor to zero and solve for x :

$\begin{gathered} x+3=0 \\ x=-3 \end{gathered}$

3rd step : Is to do synthetic division by using only the coefficients of the dividend and the value of x in the divisor.

Note that the operation in this process is multiplication and addition.

First is to bring down 2 and multiply it by -3, you will get -6 in the 2nd column.

Perform addition and multiply it again to -3 until the last term.

we have 2, -6, 18 and -52

These are the coefficients of the quotient.

and the variables will be :

$2x^2-6x+18$

we have a remainder of -52

To express the remainder as an algebraic expression, divide the remainder with the divisor.

and this will be :

$-\frac{52}{x+3}$

Putting all together, the answer is :

$2x^2-6x+18-\frac{52}{x+3}$