Add the two polynomials:

To add the two polynomials \( (4x^3-2x^2+6) \) and \( (4x^3-5x^2+2x-1) \), we will combine like terms.

1. Start by writing the two polynomials vertically:

\[ \begin{array}{r} 4x^3 - 2x^2 + 6 \

• (4x^3 - 5x^2 + 2x - 1) \ \hline \end{array} \]

2. Now, we will add the coefficients of each term:

• For \( x^3 \) terms: \( 4x^3 + 4x^3 = 8x^3 \)
• For \( x^2 \) terms: \( -2x^2 - 5x^2 = -7x^2 \)
• For \( x \) terms: \( 0 + 2x = 2x \)
• For constant terms: \( 6 - 1 = 5 \)

3. Putting it all together, we get:

\[ 8x^3 - 7x^2 + 2x + 5 \]

Looking at the provided answer choices, the correct answer is: B: \( 8x^3 - 7x^2 + 2x + 5 \)