The polynomial $x^3+64$ is an example of which type of polynomial?

• A. Difference of cubes
• B. Sum of cubes
• C. Perfect square trinomial
• D. Difference of squares

Answer: (B)

Verified step by step guidance

1. Identify the given polynomial: \(x^{3} + 64\).
2. Recognize that \$64\( can be written as \)4^{3}\(, so the polynomial is \)x^{3} + 4^{3}$.
3. Recall that a sum of cubes has the general form \(a^{3} + b^{3}\), where both terms are perfect cubes.
4. Compare the polynomial to the sum of cubes form and confirm that it matches because both \(x^{3}\) and \$4^{3}$ are cubes.
5. Conclude that the polynomial \(x^{3} + 64\) is an example of a sum of cubes.