Question

use the long division method to find the result when $2x^{3}+11x^{2}+7x + 1$ is divided by $2x + 1$.

Explanation:

Step1: Divide first - term of dividend by first - term of divisor

Divide $2x^{3}$ by $2x$: $\frac{2x^{3}}{2x}=x^{2}$.

Step2: Multiply divisor by result and subtract from dividend

Multiply $2x + 1$ by $x^{2}$: $x^{2}(2x + 1)=2x^{3}+x^{2}$. Subtract from $2x^{3}+11x^{2}+7x + 1$: $(2x^{3}+11x^{2}+7x + 1)-(2x^{3}+x^{2}) = 10x^{2}+7x+1$.

Step3: Divide first - term of new dividend by first - term of divisor

Divide $10x^{2}$ by $2x$: $\frac{10x^{2}}{2x}=5x$.

Step4: Multiply divisor by result and subtract from new dividend

Multiply $2x + 1$ by $5x$: $5x(2x + 1)=10x^{2}+5x$. Subtract from $10x^{2}+7x + 1$: $(10x^{2}+7x + 1)-(10x^{2}+5x)=2x + 1$.

Step5: Divide first - term of new dividend by first - term of divisor

Divide $2x$ by $2x$: $\frac{2x}{2x}=1$.

Step6: Multiply divisor by result and subtract from new dividend

Multiply $2x + 1$ by $1$: $1(2x + 1)=2x + 1$. Subtract from $2x + 1$: $(2x + 1)-(2x + 1)=0$.

Answer:

$x^{2}+5x + 1$