Which example correctly demonstrates polynomial addition?

Question

A) (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
B) (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10
C) 2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10
D) 2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8

Answer 1

To determine which example correctly demonstrates polynomial addition, let's perform the addition for each option:

1. A)
   \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \] Combining like terms: \[ (2x^2 + 3x^2) + (6x + 3x) + (1 + 9) = 5x^2 + 9x + 10 \] This statement is correct.

2. B)
   \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \] Combining like terms again: \[ (2x^2 + 3x^2) + (6x + 3x) + (1 + 9) = 5x^2 + 9x + 10 \] However, B states it equals \( 5x^4 + 9x^2 + 10 \), which is incorrect.

3. C)
   \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \] Again, combining like terms: \[ 5x^2 + 9x + 10 \] But C states it equals \( 13x^2 + 9x + 10 \), which is also incorrect.

4. D)
   \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \] Combining the like terms: \[ 5x^2 + 9x + 10 \] However, D claims it equals \( -x^2 + 3x - 8 \), which is incorrect as well.

Thus, the only option that correctly demonstrates polynomial addition is A):
\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]