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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:
What must be subtracted from the polynomial 8x^4 + 14x^3 + x^2 + 7x + 8 so that the resulting polynomial is exactly divisible by 4x^2 - 3x + 2?
Solution:
To solve this problem, we need to perform polynomial long division.
Step 1: Set up the division:
We want to divide the given polynomial 8x^4 + 14x^3 + x^2 + 7x + 8 by the divisor 4x^2 - 3x + 2.
Step 2: Divide the first term:
The first term of the dividend is 8x^4, and the first term of the divisor is 4x^2. Dividing these terms gives us 2x^2.
Step 3: Multiply the divisor by the quotient:
Now, we multiply 2x^2 by the divisor 4x^2 - 3x + 2. This gives us 8x^4 - 6x^3 + 4x^2.
Step 4: Subtract the result from the dividend:
Subtracting 8x^4 - 6x^3 + 4x^2 from the dividend 8x^4 + 14x^3 + x^2 + 7x + 8 gives us:
(8x^4 + 14x^3 + x^2 + 7x + 8) - (8x^4 - 6x^3 + 4x^2)
Simplifying this expression, we get: 20x^3 - 3x^2 + 7x + 8.
Step 5: Repeat the process:
We repeat the steps above with the new polynomial 20x^3 - 3x^2 + 7x + 8 as the dividend.
Step 6: Divide the first term:
The first term of the new dividend is 20x^3, and the first term of the divisor is 4x^2. Dividing these terms gives us 5x.
Step 7: Multiply the divisor by the quotient:
Now, we multiply 5x by the divisor 4x^2 - 3x + 2. This gives us 20x^3 - 15x^2 + 10x.
Step 8: Subtract the result from the dividend:
Subtracting 20x^3 - 15x^2 + 10x from the dividend 20x^3 - 3x^2 + 7x + 8 gives us:
(20x^3 - 3x^2 + 7x + 8) - (20x^3 - 15x^2 + 10x)
Simplifying this expression, we get: 12x^2 - 3x + 8.
Step 9: Finalize the division:
Since the degree of the new dividend 12x^2 - 3x + 8 is less than the degree of the divisor 4x^2 - 3x + 2
What must be subtracted from the polynomial 8x^4 + 14x^3 + x^2 + 7x + 8 so that the resulting polynomial is exactly divisible by 4x^2 - 3x + 2?
Solution:
To solve this problem, we need to perform polynomial long division.
Step 1: Set up the division:
We want to divide the given polynomial 8x^4 + 14x^3 + x^2 + 7x + 8 by the divisor 4x^2 - 3x + 2.
Step 2: Divide the first term:
The first term of the dividend is 8x^4, and the first term of the divisor is 4x^2. Dividing these terms gives us 2x^2.
Step 3: Multiply the divisor by the quotient:
Now, we multiply 2x^2 by the divisor 4x^2 - 3x + 2. This gives us 8x^4 - 6x^3 + 4x^2.
Step 4: Subtract the result from the dividend:
Subtracting 8x^4 - 6x^3 + 4x^2 from the dividend 8x^4 + 14x^3 + x^2 + 7x + 8 gives us:
(8x^4 + 14x^3 + x^2 + 7x + 8) - (8x^4 - 6x^3 + 4x^2)
Simplifying this expression, we get: 20x^3 - 3x^2 + 7x + 8.
Step 5: Repeat the process:
We repeat the steps above with the new polynomial 20x^3 - 3x^2 + 7x + 8 as the dividend.
Step 6: Divide the first term:
The first term of the new dividend is 20x^3, and the first term of the divisor is 4x^2. Dividing these terms gives us 5x.
Step 7: Multiply the divisor by the quotient:
Now, we multiply 5x by the divisor 4x^2 - 3x + 2. This gives us 20x^3 - 15x^2 + 10x.
Step 8: Subtract the result from the dividend:
Subtracting 20x^3 - 15x^2 + 10x from the dividend 20x^3 - 3x^2 + 7x + 8 gives us:
(20x^3 - 3x^2 + 7x + 8) - (20x^3 - 15x^2 + 10x)
Simplifying this expression, we get: 12x^2 - 3x + 8.
Step 9: Finalize the division:
Since the degree of the new dividend 12x^2 - 3x + 8 is less than the degree of the divisor 4x^2 - 3x + 2
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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?
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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? 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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