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------------------------------------------------ Question 2 of 45

Which of the following represents the sum of the polynomials below?

[tex]\[\left(6x^3 + 2x^2 + 9x\right) + \left(-2x^3 + 5x^2 + 3x\right)\][/tex]

A. [tex]$4x^3 + 7x^2 + 12x$[/tex]

B. [tex]$4x^3 + 7x^2 + 6x$[/tex]

C. [tex]$8x^3 + 7x^2 + 12x$[/tex]

D. [tex]$4x^3 + 7x^2 + 12$[/tex]

To find the sum of the given polynomials [tex]$(6x^3 + 2x^2 + 9x) + (-2x^3 + 5x^2 + 3x)$[/tex], follow these steps:

1. Identify the like terms in each polynomial.
- For [tex]$x^3$[/tex] terms: [tex]$6x^3$[/tex] and [tex]$-2x^3$[/tex]
- For [tex]$x^2$[/tex] terms: [tex]$2x^2$[/tex] and [tex]$5x^2$[/tex]
- For [tex]$x$[/tex] terms: [tex]$9x$[/tex] and [tex]$3x$[/tex]

2. Add the like terms together.
- For the [tex]$x^3$[/tex] terms: [tex]$6x^3 + (-2x^3) = 6x^3 - 2x^3 = 4x^3$[/tex]
- For the [tex]$x^2$[/tex] terms: [tex]$2x^2 + 5x^2 = 7x^2$[/tex]
- For the [tex]$x$[/tex] terms: [tex]$9x + 3x = 12x$[/tex]

3. Combine these results to form the resulting polynomial sum.
- Which gives us: [tex]$4x^3 + 7x^2 + 12x$[/tex]

Thus, the sum of the polynomials [tex]$(6x^3 + 2x^2 + 9x)$[/tex] and [tex]$(-2x^3 + 5x^2 + 3x)$[/tex] is:

Answer:
A. [tex]$4x^3 + 7x^2 + 12x$[/tex]