Question

question
use synthetic division to find the result when ( x^4 - 8x^3 + 21x^2 - 10x - 24 ) is divided by ( x - 3 ).

Explanation:

Step1: Set up synthetic division

Write root 3, coefficients: $1, -8, 21, -10, -24$

Step2: Bring down leading coefficient

$\downarrow \quad 3 \quad -15 \quad 18 \quad 24$
$\quad\quad 1 \quad -5 \quad 6 \quad 8 \quad \quad 0$

Step3: Form quotient polynomial

Quotient: $x^3 -5x^2 +6x +8$, remainder $0$

Answer:

$x^3 - 5x^2 + 6x + 8$