Question

polynomial long division (level 1)
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use the long division method to find the result when $8x^3 + 8x^2 + 12x + 5$ is divided by $2x + 1$.
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Explanation:

Step1: Divide leading terms

$\frac{8x^3}{2x} = 4x^2$

Step2: Multiply divisor by result

$4x^2(2x+1) = 8x^3 + 4x^2$

Step3: Subtract from dividend

$(8x^3+8x^2+12x+5)-(8x^3+4x^2) = 4x^2+12x+5$

Step4: Divide new leading terms

$\frac{4x^2}{2x} = 2x$

Step5: Multiply divisor by result

$2x(2x+1) = 4x^2 + 2x$

Step6: Subtract from new dividend

$(4x^2+12x+5)-(4x^2+2x) = 10x+5$

Step7: Divide leading terms again

$\frac{10x}{2x} = 5$

Step8: Multiply divisor by result

$5(2x+1) = 10x+5$

Step9: Subtract to find remainder

$(10x+5)-(10x+5) = 0$

Answer:

$4x^2 + 2x + 5$