Answer:
[tex]3x^2-11x+34[/tex]
Explanation:
Given the division below:
[tex](3x^3-2x^2+x-4)\div(x+3)[/tex]
First, set the denominator equal to 0 and solve for x.
[tex]\begin{gathered} x+3=0 \\ x=-3 \end{gathered}[/tex]
Next, set the synthetic division table as shown below:
• Bring down the leading coefficient, 3.
,
• Then multiply 3 by -3, write the result in the next column and add.
Repeat the process until you get the sum of the last column.
Therefore:
[tex]\frac{3x^3-2x^2+x-4}{x+3}=3x^2-11x+34-\frac{106}{x+3}[/tex]
Following the instruction in the question, we ignore the remainder and write:
[tex]\frac{3x^3-2x^2+x-4}{x+3}=\frac{3x^3-2x^2+x-4}{x+3}=3x^2-11x+34[/tex]
