Which example correctly demonstrates polynomial subtraction?(1 point)

Question

Responses

(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)=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

Answer 1

To determine which example correctly demonstrates polynomial subtraction, let's perform the subtraction of the polynomials step by step.

We start with the expression:

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

When we distribute the negative sign across the second polynomial, we get:

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

Now, we combine like terms:

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

Putting it all together:

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

Now let's compare this result with the provided options:

1. First option: \(-5x^2 + 3x - 8\) (incorrect)
2. Second option: \(x^2 + 3x + 8\) (incorrect)
3. Third option: \(5x^2 + 9x + 10\) (incorrect)
4. Fourth option: \(-x^2 + 3x - 8\) (correct)

Thus, the correct example that demonstrates polynomial subtraction is:

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