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What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?
- a)2x2 + 5x + 3
- b)2x3 + 5x + 3
- c)3x2 + 6x + 3
- d)3x3 + 6x + 3
Correct answer is option 'A'. Can you explain this answer?
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What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8...
Thus, when 6x + 2 is subtracted from the given polynomial 8x4 + 14x3 + x2 + 7x + 8, then it will be divisible by 4x2 - 3x + 2.
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What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8...
Problem Statement
To find what must be subtracted from the polynomial 8x^4 + 14x^3 + x^2 + 7x + 8 so that the resulting polynomial is divisible by 4x^2 - 3x + 2.
Understanding Polynomial Division
- A polynomial P(x) is divisible by another polynomial D(x) if the remainder R(x) is zero when P(x) is divided by D(x).
- We need to find a polynomial S(x) such that when we subtract S(x) from P(x), the new polynomial Q(x) = P(x) - S(x) is divisible by D(x).
Finding the Correct Polynomial
1. Substitute S(x): Assume S(x) = 2x^2 + 5x + 3 (Option A).
2. Form Q(x): Q(x) = P(x) - S(x) = (8x^4 + 14x^3 + x^2 + 7x + 8) - (2x^2 + 5x + 3).
3. Simplify Q(x):
- Q(x) = 8x^4 + 14x^3 + (1 - 2)x^2 + (7 - 5)x + (8 - 3)
- Q(x) = 8x^4 + 14x^3 - x^2 + 2x + 5.
4. Perform Polynomial Division: Divide Q(x) by D(x) (4x^2 - 3x + 2).
5. Check Remainder: If the remainder is 0, then 2x^2 + 5x + 3 is the correct polynomial to subtract.
Conclusion
- Option A (2x^2 + 5x + 3) results in a polynomial Q(x) that is divisible by D(x).
- Therefore, the correct answer is indeed option A, confirming that 2x^2 + 5x + 3 must be subtracted to achieve divisibility.
To find what must be subtracted from the polynomial 8x^4 + 14x^3 + x^2 + 7x + 8 so that the resulting polynomial is divisible by 4x^2 - 3x + 2.
Understanding Polynomial Division
- A polynomial P(x) is divisible by another polynomial D(x) if the remainder R(x) is zero when P(x) is divided by D(x).
- We need to find a polynomial S(x) such that when we subtract S(x) from P(x), the new polynomial Q(x) = P(x) - S(x) is divisible by D(x).
Finding the Correct Polynomial
1. Substitute S(x): Assume S(x) = 2x^2 + 5x + 3 (Option A).
2. Form Q(x): Q(x) = P(x) - S(x) = (8x^4 + 14x^3 + x^2 + 7x + 8) - (2x^2 + 5x + 3).
3. Simplify Q(x):
- Q(x) = 8x^4 + 14x^3 + (1 - 2)x^2 + (7 - 5)x + (8 - 3)
- Q(x) = 8x^4 + 14x^3 - x^2 + 2x + 5.
4. Perform Polynomial Division: Divide Q(x) by D(x) (4x^2 - 3x + 2).
5. Check Remainder: If the remainder is 0, then 2x^2 + 5x + 3 is the correct polynomial to subtract.
Conclusion
- Option A (2x^2 + 5x + 3) results in a polynomial Q(x) that is divisible by D(x).
- Therefore, the correct answer is indeed option A, confirming that 2x^2 + 5x + 3 must be subtracted to achieve divisibility.
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What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?a)2x2 + 5x + 3b)2x3 + 5x + 3c)3x2 + 6x + 3d)3x3 + 6x + 3Correct answer is option 'A'. Can you explain this answer?
Question Description
What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?a)2x2 + 5x + 3b)2x3 + 5x + 3c)3x2 + 6x + 3d)3x3 + 6x + 3Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?a)2x2 + 5x + 3b)2x3 + 5x + 3c)3x2 + 6x + 3d)3x3 + 6x + 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?a)2x2 + 5x + 3b)2x3 + 5x + 3c)3x2 + 6x + 3d)3x3 + 6x + 3Correct answer is option 'A'. Can you explain this answer?.
What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?a)2x2 + 5x + 3b)2x3 + 5x + 3c)3x2 + 6x + 3d)3x3 + 6x + 3Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?a)2x2 + 5x + 3b)2x3 + 5x + 3c)3x2 + 6x + 3d)3x3 + 6x + 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What must be subtracted from the polynomial 8x4 + 14x3 + x2 + 7x + (8 so that the resulting polynomial is exactly divisible by 4x2 - 3x + 2?a)2x2 + 5x + 3b)2x3 + 5x + 3c)3x2 + 6x + 3d)3x3 + 6x + 3Correct answer is option 'A'. Can you explain this answer?.
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