Question

question
use the long division method to find the result when $6x^3 + 23x^2 + 18x + 4$ is divided by $2x + 1$.

Explanation:

Step1: Divide leading terms

$\frac{6x^3}{2x} = 3x^2$
Multiply divisor by $3x^2$: $3x^2(2x+1)=6x^3+3x^2$
Subtract from dividend:
$(6x^3+23x^2+18x+4)-(6x^3+3x^2)=20x^2+18x+4$

Step2: Divide new leading terms

$\frac{20x^2}{2x}=10x$
Multiply divisor by $10x$: $10x(2x+1)=20x^2+10x$
Subtract:
$(20x^2+18x+4)-(20x^2+10x)=8x+4$

Step3: Divide final leading terms

$\frac{8x}{2x}=4$
Multiply divisor by $4$: $4(2x+1)=8x+4$
Subtract:
$(8x+4)-(8x+4)=0$

Answer:

$3x^2 + 10x + 4$