Divide: Left Parenthesis negative 4 x-cubed plus 35 x plus 25 Right Parenthesis divided by Left Parenthesis negative 2 x minus 5 Right Parenthesis
A. Negative 2 x-squared minus 5 x plus 5
B. 2 x-squared minus 5 x minus 5
C. Negative 2 x-squared plus 5 x minus 5
D. 2 x-squared plus 5 x plus 5
AAAaannndd the bot gets it wrong yet again!
Left Parenthesis negative 4 x-cubed plus 35 x plus 25 Right Parenthesis divided by Left Parenthesis negative 2 x minus 5 Right Parenthesis
(-4x^3+35x+25)/(-2x-5) = 2x^2-5x-5
So, B
I apologize for the mistake in my previous response. You are correct that the answer is B. Thank you for letting me know and correcting me.
To divide the given expression, we can use polynomial long division. Here's how to do it step by step:
1. Write the dividend (negative 4x^3 + 35x + 25) and the divisor (negative 2x - 5) in long division form.
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-2x - 5 | -4x^3 + 35x + 25
2. Divide the first term of the dividend by the first term of the divisor to get the quotient's first term. In this case, -4x^3 ÷ -2x gives us 2x^2.
2x^2
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-2x - 5 | -4x^3 + 35x + 25
3. Multiply the divisor by the quotient's first term to get the product. In this case, -2x - 5 multiplied by 2x^2 gives us -4x^3 - 10x^2.
2x^2
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-2x - 5 | -4x^3 + 35x + 25
4x^3 + 10x^2
4. Subtract the product from the dividend and bring down the next term. In this case, subtracting -4x^3 - 10x^2 from -4x^3 + 35x + 25 gives us 45x^2 + 35x + 25.
2x^2
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-2x - 5 | -4x^3 + 35x + 25
4x^3 + 10x^2
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45x^2 + 35x + 25
5. Repeat steps 2-4 until you have no terms left to bring down. In this case, we can divide 45x^2 by -2x to get -22.5x and multiply it by -2x - 5 to get -45x^2 - 112.5x. Subtracting this from 45x^2 + 35x + 25 gives us 147.5x + 25.
2x^2 - 22.5x
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-2x - 5 | -4x^3 + 35x + 25
4x^3 + 10x^2
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45x^2 + 35x + 25
- 45x^2 - 112.5x
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147.5x + 25
6. There are no more terms to bring down, so the final quotient is 2x^2 - 22.5x.
Thus, the correct answer is A. Negative 2 x-squared minus 5 x plus 5.