How do you divide #(x^3+7x^24x1)/(3x1) #?
Degree higher than < degree lower.
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To divide (x^3+7x^24x1) by (3x1), you can use long division. Here are the steps:

Divide the first term of the numerator (x^3) by the first term of the denominator (3x). The result is (1/3)x^2.

Multiply the entire denominator (3x1) by the result from step 1, which is (1/3)x^2. This gives you (1/3)x^3  (1/3)x^2.

Subtract the result from step 2 from the original numerator (x^3+7x^24x1). This gives you (7/3)x^2  4x  1.

Bring down the next term from the original numerator, which is 4x.

Divide the first term of the new numerator ((7/3)x^2) by the first term of the denominator (3x). The result is (7/9)x.

Multiply the entire denominator (3x1) by the result from step 5, which is (7/9)x. This gives you (7/9)x^2  (7/9)x.

Subtract the result from step 6 from the new numerator ((7/3)x^2  4x  1). This gives you (4/9)x  1.

Bring down the next term from the original numerator, which is 1.

Divide the first term of the new numerator ((4/9)x) by the first term of the denominator (3x). The result is (4/27).

Multiply the entire denominator (3x1) by the result from step 9, which is (4/27). This gives you (4/27)x  (4/27).

Subtract the result from step 10 from the new numerator ((4/9)x  1). This gives you (4/27) + (4/27).

The final result of the division is (1/3)x^2 + (7/9)x  (4/27).
Therefore, (x^3+7x^24x1)/(3x1) = (1/3)x^2 + (7/9)x  (4/27).
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