Question

polynomial long division (level 1)
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use the long division method to find the result when $8x^3 + 30x^2 + 30x + 9$ is divided by $4x + 3$.
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Explanation:

Step1: Divide leading terms

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

Step2: Multiply divisor by result

$2x^2(4x+3) = 8x^3 + 6x^2$

Step3: Subtract from dividend

$(8x^3+30x^2+30x+9) - (8x^3+6x^2) = 24x^2+30x+9$

Step4: Divide new leading terms

$\frac{24x^2}{4x} = 6x$

Step5: Multiply divisor by result

$6x(4x+3) = 24x^2 + 18x$

Step6: Subtract from current polynomial

$(24x^2+30x+9) - (24x^2+18x) = 12x+9$

Step7: Divide leading terms again

$\frac{12x}{4x} = 3$

Step8: Multiply divisor by result

$3(4x+3) = 12x+9$

Step9: Subtract to find remainder

$(12x+9) - (12x+9) = 0$

Answer:

$2x^2 + 6x + 3$