To correctly demonstrate polynomial subtraction, you need to show an example where one polynomial is subtracted from another. Here's a simple example:
Let: \[ P(x) = 3x^2 + 5x + 4 \] \[ Q(x) = 2x^2 + 3x + 1 \]
The subtraction of \( Q(x) \) from \( P(x) \) can be written as: \[ P(x) - Q(x) = (3x^2 + 5x + 4) - (2x^2 + 3x + 1) \]
Now, performing the subtraction step-by-step:
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Distribute the negative sign to \( Q(x) \): \[ P(x) - Q(x) = 3x^2 + 5x + 4 - 2x^2 - 3x - 1 \]
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Combine like terms:
- \( 3x^2 - 2x^2 = 1x^2 \)
- \( 5x - 3x = 2x \)
- \( 4 - 1 = 3 \)
Putting it all together gives: \[ P(x) - Q(x) = 1x^2 + 2x + 3 \]
This example shows a clear process of polynomial subtraction.