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Which example correctly demonstrates polynomial subtraction?(1 point) Responses (2x2+6x+1)−(3x2+3x+9)=5x2+9x+10 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 5 x squared plus 9 x plus 10 (2x2+6x+1)−(3x2+3x+9)=x2+3x+8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 6 x minus 4 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 4 right parenthesis (2x2+6x+1)−(3x2+3x+9)=−x2+3x−8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals negative x squared plus 3 x minus 8 (2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8

Take off the subscript

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To correctly demonstrate polynomial subtraction, we need to subtract the second polynomial from the first and combine like terms appropriately. Let's break down the subtraction for the given example:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

First, distribute the negative sign across the second polynomial:

\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

Now, combine like terms:

1. Combine the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
2. Combine the \(x\) terms: \(6x - 3x = 3x\)
3. Combine the constant terms: \(1 - 9 = -8\)

Putting it all together, we get:

\[
-x^2 + 3x - 8
\]

Thus, the correct answer is:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]

So, the correct example demonstrating polynomial subtraction is:

**(2x² + 6x + 1) - (3x² + 3x + 9) = -x² + 3x - 8**.