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The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________
- a)10x3 - 15x2 - 10x - 20
- b)10x3 + 15x2 + 10x + 20
- c)-10x3 - 15x2 + 10x + 20
- d)-10x3 + 15x2 + 10x + 20
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and rem...
We know that,
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
f(x) = 5x2 × (2x + 3) + 10x + 20
f(x) = 10x3 + 15x2 + 10x + 20
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
f(x) = 5x2 × (2x + 3) + 10x + 20
f(x) = 10x3 + 15x2 + 10x + 20
Most Upvoted Answer
The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and rem...
The given polynomial is divided by the divisor 5x^2, and the quotient is 2x + 3 with a remainder of 10x - 20. We need to find the original polynomial.
To solve this problem, we can use the division algorithm for polynomials.
The division algorithm states that any polynomial f(x) can be divided by a polynomial g(x) to give a quotient q(x) and a remainder r(x), such that:
f(x) = g(x) * q(x) + r(x)
Here, f(x) is the original polynomial, g(x) is the divisor, q(x) is the quotient, and r(x) is the remainder.
In this case, we have:
f(x) = (5x^2) * (2x + 3) + (10x - 20)
To find the original polynomial, we multiply the divisor (5x^2) by the quotient (2x + 3) and add the remainder (10x - 20).
Simplifying the expression, we get:
f(x) = 10x^3 + 15x^2 + 30x^2 + 45x - 20x - 30 + 10x - 20
Combining like terms, we have:
f(x) = 10x^3 + 45x^2 + 35x - 50
Therefore, the original polynomial is 10x^3 + 45x^2 + 35x - 50.
Now, let's check which option matches the original polynomial:
a) 10x^3 - 15x^2 - 10x - 20
b) -10x^3 - 15x^2 + 10x + 20
c) 10x^3 + 15x^2 + 10x + 20
d) -10x^3 + 15x^2 + 10x + 20
From the calculations above, we can see that option B (-10x^3 - 15x^2 + 10x + 20) matches the original polynomial 10x^3 + 45x^2 + 35x - 50.
Therefore, the correct answer is option B.
To solve this problem, we can use the division algorithm for polynomials.
The division algorithm states that any polynomial f(x) can be divided by a polynomial g(x) to give a quotient q(x) and a remainder r(x), such that:
f(x) = g(x) * q(x) + r(x)
Here, f(x) is the original polynomial, g(x) is the divisor, q(x) is the quotient, and r(x) is the remainder.
In this case, we have:
f(x) = (5x^2) * (2x + 3) + (10x - 20)
To find the original polynomial, we multiply the divisor (5x^2) by the quotient (2x + 3) and add the remainder (10x - 20).
Simplifying the expression, we get:
f(x) = 10x^3 + 15x^2 + 30x^2 + 45x - 20x - 30 + 10x - 20
Combining like terms, we have:
f(x) = 10x^3 + 45x^2 + 35x - 50
Therefore, the original polynomial is 10x^3 + 45x^2 + 35x - 50.
Now, let's check which option matches the original polynomial:
a) 10x^3 - 15x^2 - 10x - 20
b) -10x^3 - 15x^2 + 10x + 20
c) 10x^3 + 15x^2 + 10x + 20
d) -10x^3 + 15x^2 + 10x + 20
From the calculations above, we can see that option B (-10x^3 - 15x^2 + 10x + 20) matches the original polynomial 10x^3 + 45x^2 + 35x - 50.
Therefore, the correct answer is option B.
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Community Answer
The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and rem...
We know that,
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
f(x) = 5x2 × (2x + 3) + 10x + 20
f(x) = 10x3 + 15x2 + 10x + 20
f(x) = q(x) × g(x) + r(x)
Where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
f(x) = 5x2 × (2x + 3) + 10x + 20
f(x) = 10x3 + 15x2 + 10x + 20
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The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________a)10x3- 15x2- 10x - 20b)10x3+ 15x2+ 10x + 20c)-10x3- 15x2+ 10x + 20d)-10x3+ 15x2+ 10x + 20Correct answer is option 'B'. Can you explain this answer?
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The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________a)10x3- 15x2- 10x - 20b)10x3+ 15x2+ 10x + 20c)-10x3- 15x2+ 10x + 20d)-10x3+ 15x2+ 10x + 20Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________a)10x3- 15x2- 10x - 20b)10x3+ 15x2+ 10x + 20c)-10x3- 15x2+ 10x + 20d)-10x3+ 15x2+ 10x + 20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________a)10x3- 15x2- 10x - 20b)10x3+ 15x2+ 10x + 20c)-10x3- 15x2+ 10x + 20d)-10x3+ 15x2+ 10x + 20Correct answer is option 'B'. Can you explain this answer?.
The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________a)10x3- 15x2- 10x - 20b)10x3+ 15x2+ 10x + 20c)-10x3- 15x2+ 10x + 20d)-10x3+ 15x2+ 10x + 20Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________a)10x3- 15x2- 10x - 20b)10x3+ 15x2+ 10x + 20c)-10x3- 15x2+ 10x + 20d)-10x3+ 15x2+ 10x + 20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The polynomial (x), if the divisor is 5x2, quotient is 2x + 3, and remainder is 10x + 20 is __________a)10x3- 15x2- 10x - 20b)10x3+ 15x2+ 10x + 20c)-10x3- 15x2+ 10x + 20d)-10x3+ 15x2+ 10x + 20Correct answer is option 'B'. Can you explain this answer?.
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