To determine the sum of the given polynomials [tex]\( \left(4 x^3-2 x-9\right) + \left(2 x^3+5 x+3\right) \)[/tex], let's add them step by step.
The given polynomials are:
[tex]\[ \left(4 x^3-2 x-9\right) \][/tex]
[tex]\[ \left(2 x^3+5 x+3\right) \][/tex]
### Step 1: Add the [tex]\(x^3\)[/tex] Terms
First, we add the coefficients of [tex]\(x^3\)[/tex] terms from both polynomials:
[tex]\[ 4x^3 + 2x^3 = 6x^3 \][/tex]
### Step 2: Add the [tex]\(x\)[/tex] Terms
Next, we add the coefficients of [tex]\(x\)[/tex] terms from both polynomials:
[tex]\[ -2x + 5x = 3x \][/tex]
### Step 3: Add the Constant Terms
Finally, we add the constant terms from both polynomials:
[tex]\[ -9 + 3 = -6 \][/tex]
### Result
Putting it all together, the sum of the polynomials is:
[tex]\[ 6x^3 + 3x - 6 \][/tex]
So, the correct sum of the polynomials is:
[tex]\[ \boxed{6 x^3 + 3 x - 6} \][/tex]
