Question

question
use synthetic division to find the result when $2x^4 - 15x^3 + 27x^2 + 2x + 8$ is divided by $x - 4$.

Explanation:

Step1: Set up synthetic division

Write root 4, coefficients: $2, -15, 27, 2, 8$

Step2: Bring down leading coefficient

$\downarrow \quad \quad \quad \quad \quad \quad \quad$
$2$

Step3: Multiply and add to next coeff

$2 \times 4 = 8$; $-15 + 8 = -7$

Step4: Repeat multiply-add step

$-7 \times 4 = -28$; $27 + (-28) = -1$

Step5: Repeat multiply-add step

$-1 \times 4 = -4$; $2 + (-4) = -2$

Step6: Final multiply-add step

$-2 \times 4 = -8$; $8 + (-8) = 0$

Step7: Form quotient polynomial

Coefficients $2, -7, -1, -2$ give $2x^3 -7x^2 -x -2$, remainder $0$

Answer:

$2x^3 - 7x^2 - x - 2$ (with a remainder of $0$)