find the quotient of 2x+1/4x^2+8x+5
Since you cannot divide 4x^2 into 2x+1, the quotient would be zero with a remainder of 2x+1. Which can also be written as 0 (2x+1)/(4X^2 +8X+5)
Sorry. That cannot be reduced. Assuming you mean
(2x+1)/(4x^2+8x+5)
To find the quotient of the expression (2x + 1) divided by (4x^2 + 8x + 5), you need to perform polynomial long division. Here's a step-by-step explanation of how to do it:
1. Arrange the dividend (2x + 1) and the divisor (4x^2 + 8x + 5) in the standard form of polynomial division, with the terms in decreasing powers of x.
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4x^2 + 8x + 5 | 2x + 1
2. Divide the first term of the dividend (2x) by the first term of the divisor (4x^2). The result is (1/2x).
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4x^2 + 8x + 5 | 2x + 1
-(1/2x)
3. Multiply the divisor (4x^2 + 8x + 5) by the result obtained in step 2 (1/2x), and write the product below the dividend, aligned with the variable term.
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4x^2 + 8x + 5 | 2x + 1
(1/2x^2 + x + 5/2x)
4. Subtract the product obtained in step 3 from the dividend. Write the result below, aligned with the corresponding terms.
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4x^2 + 8x + 5 | 2x + 1
(1/2x^2 + x + 5/2x)
- (1/2x^2 + x + 5/2x)
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(-7/2x + 1)
5. Bring down the next term of the dividend (-7/2x) and repeat the process until there are no terms left in the dividend.
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4x^2 + 8x + 5 | 2x + 1
(1/2x^2 + x + 5/2x)
- (1/2x^2 + x + 5/2x)
_____________________________
(-7/2x + 1)
(-7/2x +1)
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4x^2 + 8x + 5 | -7/2x + 1
6. Since there are no more terms in the dividend, we have reached the quotient, which is (-7/2x + 1).
Therefore, the quotient of (2x + 1)/(4x^2 + 8x + 5) is (-7/2x + 1).