Question

Which example correctly demonstrates polynomial subtraction?(1 point)

Answer 1

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:

1. Distribute the negative sign to \( Q(x) \):
\[ P(x) - Q(x) = 3x^2 + 5x + 4 - 2x^2 - 3x - 1 \]

2. 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.