Question

Which polynomial represents the sum below?

(-2x^3 + 4x^2 + 6) + (2x^2 + 6x + 3)

A. -x^6 + 6x^2 + 12x + 9
B. -2x^3 + 6x^2 + 6x + 9
C. -2x^5 + 10x^2 + 6x + 9
D. -2x^3 + 6x + 9
...?

Answer 1

Your answer should be B if you put all the common parts together you will find you can not simplify the equation any longer.

Answer 2

Answer:  the correct option is (B) $-2x^3+6x^2+6x+9.$

Step-by-step explanation:  We are given to select the correct polynomial that represents the following sum :

$S=(-2x^3+4x^2+6)+(2x^2+6x+3).$

To find the above sum, we need to add the coefficients of the similar powers of x.

The summation is as follows :

$S\\\\=(-2x^3+4x^2+6)+(2x^2+6x+3)\\\\=-2x^3+4x^2+6+2x^2+6x+3\\\\=-2x^3+(4+2)x^2+6x+6+3\\\\=-2x^3+6x^2+6x+9.$

Thus, the required sum is $-2x^3+6x^2+6x+9.$

Option (B) is CORRECT.