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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)=−5x2+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 2 x squared plus 6 x plus 1 minus 3 x squared minus 3 x minus 9

(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

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 perform the subtraction step by step.

Let's break down the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\):

1. **Distribute the negative sign** to the second polynomial:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

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

Putting it all together, we get:
\[
-1x^2 + 3x - 8
\]

Thus, the correct equivalent expression for the subtraction is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]

So, the correct answer from the provided options is:
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).