Question

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

Answer 1

To correctly assess polynomial subtraction, we need to subtract the terms in the second polynomial from the terms in the first polynomial.

Let's perform the subtraction step-by-step:

1. Start with the expression: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

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

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

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

Now, let's compare this result with the options given:

A. \(5x^2 + 9x + 10\) (Incorrect)
B. \(x^2 + 3x + 8\) (Incorrect)
C. \(-5x^2 + 3x - 8\) (Incorrect)
D. \(-x^2 + 3x - 8\) (Correct)

Thus, the correct answer is **D**.