Question

divide using synthetic division.
$(x^4 - 12x^2 - 5) \div (x + 3)$
the quotient is $\square$ and the remainder is $\square$.
(simplify your answers. do not factor.)

Explanation:

Step1: Identify root & coefficients

Root of divisor $x+3$ is $-3$. Coefficients of dividend $x^4+0x^3-12x^2+0x-5$: $1, 0, -12, 0, -5$

Step2: Set up synthetic division

-3 | 1   0  -12   0  -5
        -3   9   9  -27
     ----------------------
       1  -3   -3   9  -32

Step3: Write quotient & remainder

Quotient: $1x^3 -3x^2 -3x +9$, remainder: $-32$

Answer:

The quotient is $x^3 - 3x^2 - 3x + 9$ and the remainder is $-32$.