Answer:
Quotient: p + 7
Remainder: 10
Explanation:
To find the quotient of the expression (2p² + 7p - 39) ÷ (2p - 7), we can use long division or synthetic division. Let's use long division:
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2p - 7 | 2p² + 7p - 39
We start by dividing the first term of the dividend by the first term of the divisor, which gives us 2p² ÷ 2p = p. We then multiply p by the divisor (2p - 7) and subtract it from the dividend:
p
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2p - 7 | 2p² + 7p - 39
- (2p² - 7p)
14p - 39
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2p - 7 | 2p² + 7p - 39
- (2p² - 7p)
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14p - 39
We repeat the process by dividing the first term of the new dividend (14p - 39) by the first term of the divisor (2p - 7). This gives us (14p - 39) ÷ (2p - 7) = 7. We then multiply 7 by the divisor (2p - 7) and subtract it from the new dividend:
p + 7
____________________
2p - 7 | 2p² + 7p - 39
- (2p² - 7p)
___________
14p - 39
- (14p - 49)
___________
10
We are left with a remainder of 10. Therefore, the quotient is p + 7 with a remainder of 10.
Quotient: p + 7
Remainder: 10
Hope this helps!