x^6 + 5x^3 – 24) ÷ (x^3 – 3)
purplemath(dot)com/modules/polydiv2.htm
To divide the given polynomial expression, we can use long division.
Step 1: First, write the dividend (x^6 + 5x^3 – 24) and the divisor (x^3 – 3) in the long division format:
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x^3 – 3 | x^6 + 5x^3 – 24
Step 2: Divide the highest degree term of the dividend by the highest degree term of the divisor. In this case, divide x^6 by x^3. The result is x^3.
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x^3 – 3 | x^6 + 5x^3 – 24
-(x^6 – 3x^3)
Step 3: Multiply the divisor (x^3 – 3) by the quotient (x^3), and write the product below the dividend, making sure to align like terms.
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x^3 – 3 | x^6 + 5x^3 – 24
-(x^6 – 3x^3)
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8x^3
Step 4: Subtract the product obtained in the previous step from the original dividend.
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x^3 – 3 | x^6 + 5x^3 – 24
-(x^6 – 3x^3)
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8x^3 – 24
Step 5: Bring down the next term, which is -24, and repeat the process.
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x^3 – 3 | x^6 + 5x^3 – 24
-(x^6 – 3x^3)
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8x^3 – 24
-(8x^3 – 24)
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0
Step 6: The process is complete when the degree of the remainder is less than the degree of the divisor. In this case, the remainder is 0, so the final quotient is x^3.
Therefore, (x^6 + 5x^3 – 24) ÷ (x^3 – 3) = x^3.