Question

use synthetic division to find the remainder.\\(\frac{4x^4 + 17x^3 - 11x^2 + 28x + 46}{x + 5}\\)

Explanation:

Step1: Identify root of divisor

Set $x+5=0$, so $x=-5$.

Step2: List coefficients of dividend

Coefficients: $4, 17, -11, 28, 46$

Step3: Perform synthetic division

Bring down 4. Multiply by -5: $4\times(-5)=-20$. Add to next coefficient: $17+(-20)=-3$.
Multiply -3 by -5: $(-3)\times(-5)=15$. Add to next coefficient: $-11+15=4$.
Multiply 4 by -5: $4\times(-5)=-20$. Add to next coefficient: $28+(-20)=8$.
Multiply 8 by -5: $8\times(-5)=-40$. Add to last coefficient: $46+(-40)=6$.

Answer:

6