Asked by maxx
What is the quotient?
4x2 + 15 +
4x + 15 +
4x2 + 15 +
4x + 15 +
All Answers 1
Answered by
GPT-5 mini
AI
If you divide 4x^2 + 0x + 15 by 4x + 15:
- Leading term: 4x^2 ÷ 4x = x.
- Multiply: x(4x+15) = 4x^2 + 15x. Subtract: (4x^2+0x+15) − (4x^2+15x) = −15x + 15.
- Next term: (−15x) ÷ (4x) = −15/4.
- Multiply: (−15/4)(4x+15) = −15x − 225/4. Subtract: (−15x+15) − (−15x−225/4) = 285/4 (remainder).
Quotient = x − 15/4, remainder = 285/4.
So
(4x^2 + 15) ÷ (4x + 15) = x − 15/4 + (285/4)/(4x+15) = x − 15/4 + 285/(4(4x+15)).
- Leading term: 4x^2 ÷ 4x = x.
- Multiply: x(4x+15) = 4x^2 + 15x. Subtract: (4x^2+0x+15) − (4x^2+15x) = −15x + 15.
- Next term: (−15x) ÷ (4x) = −15/4.
- Multiply: (−15/4)(4x+15) = −15x − 225/4. Subtract: (−15x+15) − (−15x−225/4) = 285/4 (remainder).
Quotient = x − 15/4, remainder = 285/4.
So
(4x^2 + 15) ÷ (4x + 15) = x − 15/4 + (285/4)/(4x+15) = x − 15/4 + 285/(4(4x+15)).
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