Answer :
Final answer:
To divide the polynomial 3x3 + 19x2 + 13x - 20 by 3x - 2, we can use long division. The quotient is x2 + 7x + 9, and the remainder is -2.
Explanation:
To divide the polynomial 3x3 + 19x2 + 13x - 20 by 3x - 2, we can use long division:
- Divide 3x3 by 3x, which gives x2.
- Multiply (3x - 2) by x2, which gives 3x3 - 2x2.
- Subtract this from the original polynomial, which gives 21x2 + 13x - 20.
- Divide 21x2 by 3x, which gives 7x.
- Multiply (3x - 2) by 7x, which gives 21x2 - 14x.
- Subtract this from the remaining polynomial, which gives 27x - 20.
- Divide 27x by 3x, which gives 9.
- Multiply (3x - 2) by 9, which gives 27x - 18.
- Subtract this from the remaining polynomial, which gives -2.
Therefore, the quotient is x2 + 7x + 9, and the remainder is -2.
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