To add the given polynomials, combine like terms:

The two polynomials are:

$(5x^2 - 5x + 6) + (4x^3 - 4x)$

Step 1: Write all terms in order of decreasing powers of $x$:

$4x^3 + 5x^2 - 5x - 4x + 6$

Step 2: Combine like terms:

• $4x^3$ (only term with $x^3$)
• $5x^2$ (only term with $x^2$)
• Combine $-5x$ and $-4x$: $-5x - 4x = -9x$
• $6$ (constant term)

Step 3: Write the simplified polynomial:

$4x^3 + 5x^2 - 9x + 6$

Final Answer:

The sum is $4x^3 + 5x^2 - 9x + 6$.

Do you want further clarification or an explanation of any step?

Related Questions:

1. How do you add polynomials with more than two terms?
2. What are like terms, and why is combining them important?
3. How do you subtract polynomials instead of adding them?
4. Can you explain how to multiply two polynomials?
5. How do you arrange a polynomial in standard form?

Tip:

Always line up polynomials by the powers of $x$ when adding or subtracting to avoid missing terms.