Answer :
We are given the following two polynomials:
[tex]$$
6x^3 + 2x^2 + 9x \quad \text{and} \quad -2x^3 + 5x^2 + 3x.
$$[/tex]
Step 1. Add the coefficients for the [tex]$x^3$[/tex] terms.
[tex]$$
6x^3 + (-2x^3) = (6 - 2)x^3 = 4x^3.
$$[/tex]
Step 2. Add the coefficients for the [tex]$x^2$[/tex] terms.
[tex]$$
2x^2 + 5x^2 = (2 + 5)x^2 = 7x^2.
$$[/tex]
Step 3. Add the coefficients for the [tex]$x$[/tex] terms.
[tex]$$
9x + 3x = (9 + 3)x = 12x.
$$[/tex]
Step 4. Combine the results to write the final polynomial.
[tex]$$
4x^3 + 7x^2 + 12x.
$$[/tex]
The expression that represents the sum of the given polynomials is therefore:
[tex]$$
4x^3 + 7x^2 + 12x,
$$[/tex]
which corresponds to option B.
[tex]$$
6x^3 + 2x^2 + 9x \quad \text{and} \quad -2x^3 + 5x^2 + 3x.
$$[/tex]
Step 1. Add the coefficients for the [tex]$x^3$[/tex] terms.
[tex]$$
6x^3 + (-2x^3) = (6 - 2)x^3 = 4x^3.
$$[/tex]
Step 2. Add the coefficients for the [tex]$x^2$[/tex] terms.
[tex]$$
2x^2 + 5x^2 = (2 + 5)x^2 = 7x^2.
$$[/tex]
Step 3. Add the coefficients for the [tex]$x$[/tex] terms.
[tex]$$
9x + 3x = (9 + 3)x = 12x.
$$[/tex]
Step 4. Combine the results to write the final polynomial.
[tex]$$
4x^3 + 7x^2 + 12x.
$$[/tex]
The expression that represents the sum of the given polynomials is therefore:
[tex]$$
4x^3 + 7x^2 + 12x,
$$[/tex]
which corresponds to option B.
