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Answer :
Final answer:
To divide the polynomial (6x³+19x²+22x+3) by (3x+2), use long division to obtain a quotient of 2x²+5x+4 with a remainder of -5.
Explanation:
To divide the polynomial (6x³+19x²+22x+3) by (3x+2), we can use long division. Here is the step-by-step process:
- Divide 6x³ by 3x: the result is 2x².
- Multiply 2x² by (3x+2): the result is 6x³+4x².
- Subtract 6x³+4x² from 6x³+19x²: the result is 15x².
- Bring down the next term: 22x.
- Divide 15x² by 3x: the result is 5x.
- Multiply 5x by (3x+2): the result is 15x²+10x.
- Subtract 15x²+10x from 15x²+22x: the result is 12x.
- Bring down the next term: 3.
- Divide 12x by 3x: the result is 4.
- Multiply 4 by (3x+2): the result is 12x+8.
- Subtract 12x+8 from 12x+3: the result is -5.
Therefore, the quotient of (6x³+19x²+22x+3) ÷ (3x+2) is 2x²+5x+4 with a remainder of -5.
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