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:

$6$