To perform long division on the polynomial \(2x^2 + 9z - 35\), you will need to divide it by another polynomial. However, it seems you are only providing one polynomial. Long division is typically applied when dividing a polynomial by another polynomial (such as dividing \(2x^2 + 9z - 35\) by a polynomial like \(ax + b\)).
Let’s assume you want to divide \(2x^2 + 9z - 35\) by a polynomial \(d(x)\). Here's a general outline of how to proceed with polynomial long division:
Step-by-step Example of Polynomial Long Division
Let's say we want to divide \(2x^2 + 9z - 35\) by \(x - 3\). Here are the steps:
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Set Up the Division: Write the dividend (the polynomial to be divided) and the divisor (the polynomial to divide by) in long division format.
____________ x - 3 | 2x^2 + 0x + 9z - 35 -
Divide the Leading Term: Divide the leading term of the dividend (which is \(2x^2\)) by the leading term of the divisor (which is \(x\)). \[ \frac{2x^2}{x} = 2x \]
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Multiply and Subtract: Multiply the entire divisor by this result \(2x\) and subtract this product from the original polynomial. \[ 2x(x - 3) = 2x^2 - 6x \] Now subtract: \[ (2x^2 + 0x + 9z - 35) - (2x^2 - 6x) = 6x + 9z - 35 \]
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Repeat the Process: Now, divide the leading term again. \[ \frac{6x}{x} = 6 \] Multiply and subtract: \[ 6(x - 3) = 6x - 18 \] Now subtract: \[ (6x + 9z - 35) - (6x - 18) = 9z - 17 \]
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Final Result: The division gives us: \[ 2x + 6 + \frac{9z - 17}{x - 3} \]
Summary:
So, dividing \(2x^2 + 9z - 35\) by \(x - 3\) gives: \[ 2x + 6 + \frac{9z - 17}{x - 3} \]
If you had a different polynomial or divisor in mind, you can follow the same process by adjusting based on that divisor. Please provide the divisor you want to use if you'd like more specific instructions!
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