Question

Use synthetic division to find the quotient and remainder.

$x^4+13x^2+13x+3$is divided by$x+3$

Short answer

The quotient is $x^3-3x^2+22x+53$and the remainder is $-156$.

Step-by-step solution

Step 1. Given information.

$x^4+13x^2+13x+3$is divided by$x+3$

Step 2. Write the dividend with decreasing power of x.

$x^4+0x^3+13x^2+13x+13$

Step 3. Write the coefficients of the terms as the first row of the synthetic division. 

Write the divisor form of $x-c$that is $x-\left(-3\right)$.

$\overline{)-3}1013133$

Step 4. Bring down the first coefficient to the third row and multiply the coefficients by the divisor and place the result in the second row and add the column and put the result in the third row. 

$$\begin{gathered} \overline{)-3}1013133 \\ -39-66-159 \\ \overline{1-32253\overline{)-156}} \end{gathered}$$

Step 4. Simplified answer. 

The coefficients of the quotient are $1,-3,22,53$.

The quotient isrole="math" localid="1644402541115" $x^3-3x^2+22x+53$and the remainder is$-156$.