To divide the polynomial 6x^3 + 4x^2 - 2x + 5 by 3x^2 + 2x + 1 using long division, follow these steps:
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3x^2 + 2x + 1 | 6x^3 + 4x^2 - 2x + 5
Step 1: Divide the highest degree term of the dividend (6x^3) by the highest degree term of the divisor (3x^2) to get 2x, which is then placed above the line.
2x
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3x^2 + 2x + 1 | 6x^3 + 4x^2 - 2x + 5
Step 2: Multiply the divisor (3x^2 + 2x + 1) by the quotient (2x) and subtract the result from the dividend (6x^3 + 4x^2 - 2x + 5).
2x (3x^2 + 2x + 1)
6x^3 + 4x^2 + 2x
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-6x^3 - 4x^2 + 2x + 5
Step 3: Bring down the next term from the dividend (-2x + 5) to continue the division process.
2x (3x^2 + 2x + 1)
6x^3 + 4x^2 + 2x
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-6x^3 - 4x^2 + 2x + 5
-2x + 5
Step 4: Repeat steps 1 and 2 with the new dividend (-6x^3 - 4x^2 + 2x + 5).
2x (3x^2 + 2x + 1)
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-6x^3 - 4x^2 + 2x + 5
-6x^3 - 4x^2 - 2x
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4x + 5
Step 5: Since the degree of the new dividend (4x + 5) is less than the degree of the divisor (3x^2 + 2x + 1), we have a remainder of 4x + 5.
Therefore, the quotient is 2x and the remainder is 4x + 5.
6x^3+4x^2-2x+5 divided by 3x^2+2x+1
Using the long division method
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