Question

Which example correctly demonstrates polynomial subtraction?(1 point) Responses
A. (2x^2+6x+1)−(3x^2+3x+9)=5x2+9x+10
B. (2x^2+6x+1)−(3x^2+3x+9)=−x2+3x−8
C. (2x^2+6x+1)−(3x^2+3x+9)=−5x2+3x−8
D. (2x^2+6x+1)−(3x^2+3x+9)=x2+3x+8

Answer 1

To demonstrate polynomial subtraction, you need to subtract each corresponding term of the polynomial being subtracted from the polynomial that is being subtracted from.

Let's calculate the subtraction of the polynomials in the options:

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

We can distribute the negative sign through the second polynomial:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

Now, combine the like terms:
- For \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
- For \(x\) terms: \(6x - 3x = 3x\)
- For constant terms: \(1 - 9 = -8\)

Putting it all together:
\[
= -x^2 + 3x - 8
\]

Comparing this result to the options given:
- A. Incorrect
- B. Correct: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\)
- C. Incorrect
- D. Incorrect

Thus, the correct answer is B. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).