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If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1, the remainder comes out to be ax + b. What is the value of a and b?
- a)a = 1, b = 2
- b)a = 2, b = 1
- c)a = -2, b = 1
- d)a = -1, b = -2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another pol...
To find the remainder when the polynomial 6x^4 + 8x^3 + 17x^2 + 21x + 7 is divided by the polynomial 3x^2 + 4x + 1, we can use polynomial long division.
1. Polynomial Division:
Dividing the first term of the dividend (6x^4) by the first term of the divisor (3x^2), we get 2x^2 as the first term of the quotient. Multiplying the entire divisor by 2x^2, we get 6x^4 + 8x^3 + 2x^2. Subtracting this from the dividend, we get a new polynomial to divide:
6x^4 + 8x^3 + 17x^2 + 21x + 7
÷ 3x^2 + 4x + 1
______________________
= 2x^2 + (remainder)
2. Next Term:
Now, dividing the first term of the new polynomial (8x^3) by the first term of the divisor (3x^2), we get 2.66x as the next term of the quotient. Multiplying the entire divisor by 2.66x, we get 7.98x^3 + 10.64x^2 + 2.66x. Subtracting this from the new polynomial, we get another new polynomial to divide:
6x^4 + 8x^3 + 17x^2 + 21x + 7
÷ 3x^2 + 4x + 1
______________________
= 2x^2 + 2.66x + (remainder)
3. Final Term:
Now, dividing the first term of the new polynomial (17x^2) by the first term of the divisor (3x^2), we get 5.67 as the next term of the quotient. Multiplying the entire divisor by 5.67, we get 17.01x^2 + 22.68x + 5.67. Subtracting this from the new polynomial, we get the remainder:
6x^4 + 8x^3 + 17x^2 + 21x + 7
÷ 3x^2 + 4x + 1
______________________
= 2x^2 + 2.66x + 5.67
4. Evaluating Remainder:
The remainder of the division is 2x^2 + 2.66x + 5.67. Since this is in the form ax + b, we can say that a = 2.66 and b = 5.67.
Therefore, the correct answer is option A: a = 2.66, b = 5.67.
1. Polynomial Division:
Dividing the first term of the dividend (6x^4) by the first term of the divisor (3x^2), we get 2x^2 as the first term of the quotient. Multiplying the entire divisor by 2x^2, we get 6x^4 + 8x^3 + 2x^2. Subtracting this from the dividend, we get a new polynomial to divide:
6x^4 + 8x^3 + 17x^2 + 21x + 7
÷ 3x^2 + 4x + 1
______________________
= 2x^2 + (remainder)
2. Next Term:
Now, dividing the first term of the new polynomial (8x^3) by the first term of the divisor (3x^2), we get 2.66x as the next term of the quotient. Multiplying the entire divisor by 2.66x, we get 7.98x^3 + 10.64x^2 + 2.66x. Subtracting this from the new polynomial, we get another new polynomial to divide:
6x^4 + 8x^3 + 17x^2 + 21x + 7
÷ 3x^2 + 4x + 1
______________________
= 2x^2 + 2.66x + (remainder)
3. Final Term:
Now, dividing the first term of the new polynomial (17x^2) by the first term of the divisor (3x^2), we get 5.67 as the next term of the quotient. Multiplying the entire divisor by 5.67, we get 17.01x^2 + 22.68x + 5.67. Subtracting this from the new polynomial, we get the remainder:
6x^4 + 8x^3 + 17x^2 + 21x + 7
÷ 3x^2 + 4x + 1
______________________
= 2x^2 + 2.66x + 5.67
4. Evaluating Remainder:
The remainder of the division is 2x^2 + 2.66x + 5.67. Since this is in the form ax + b, we can say that a = 2.66 and b = 5.67.
Therefore, the correct answer is option A: a = 2.66, b = 5.67.
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Community Answer
If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another pol...
3x2 + 4 x +1) 6 x4 + 8 x3 +17 x2 + 21x + 7 (2 x2 + 5
remainder = x + 2
ax + b = x + 2 (Given)
⇒ a = 1; b = 2
remainder = x + 2
ax + b = x + 2 (Given)
⇒ a = 1; b = 2
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If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1, the remainder comes out to be ax + b. What is the value of a and b?a)a = 1, b = 2b)a = 2, b = 1c)a = -2, b = 1d)a = -1, b = -2Correct answer is option 'A'. Can you explain this answer?
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