Question

divide by using synthetic division. simplify your answer as much as possible
$(-2x^{3}-10x^{2}+2x+15)\div(x+4)=\square$

Explanation:

Step1: Identify root of divisor

For $x+4=0$, root is $x=-4$

Step2: List coefficients of dividend

Coefficients: $-2, -10, 2, 15$

Step3: Perform synthetic division

Bring down $-2$. Multiply by $-4$: $(-2)(-4)=8$
Add to next coefficient: $-10+8=-2$
Multiply $-2$ by $-4$: $(-2)(-4)=8$
Add to next coefficient: $2+8=10$
Multiply $10$ by $-4$: $10(-4)=-40$
Add to last coefficient: $15+(-40)=-25$

Step4: Form quotient and remainder

Quotient: $-2x^2 -2x +10$, remainder: $-25$

Answer:

$-2x^2 - 2x + 10 - \frac{25}{x+4}$