Question

question
use the long division method to find the result when $8x^3 + 16x^2 + 16x + 5$ is divided by $2x + 1$.

Explanation:

Step1: Divide leading terms

$\frac{8x^3}{2x} = 4x^2$
Multiply divisor by $4x^2$: $4x^2(2x+1)=8x^3+4x^2$
Subtract from dividend:
$(8x^3+16x^2+16x+5)-(8x^3+4x^2)=12x^2+16x+5$

Step2: Divide new leading terms

$\frac{12x^2}{2x}=6x$
Multiply divisor by $6x$: $6x(2x+1)=12x^2+6x$
Subtract:
$(12x^2+16x+5)-(12x^2+6x)=10x+5$

Step3: Divide new leading terms

$\frac{10x}{2x}=5$
Multiply divisor by $5$: $5(2x+1)=10x+5$
Subtract:
$(10x+5)-(10x+5)=0$

Answer:

$4x^2 + 6x + 5$