To add the given polynomials $(x^2 + 6x - 8)$ and $(9x^2 - 5x + 7)$, combine like terms:

Step 1: Write the polynomials together

$(x^2 + 6x - 8) + (9x^2 - 5x + 7)$

Step 2: Group like terms

$(x^2 + 9x^2) + (6x - 5x) + (-8 + 7)$

Step 3: Add the coefficients of like terms

• $x^2 + 9x^2 = 10x^2$
• $6x - 5x = 1x$ (or simply $x$)
• $-8 + 7 = -1$

Final Answer:

$10x^2 + x - 1$

Would you like a detailed breakdown of any specific step?

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Here are 5 related questions to expand your understanding:

1. How do you subtract polynomials instead of adding them?
2. What are the rules for combining like terms in polynomials?
3. How do you simplify expressions with more variables, such as $x$ and $y$?
4. Can you solve a quadratic equation formed by adding these polynomials, like $10x^2 + x - 1 = 0$?
5. What are polynomials, and how are they classified based on their degree?

Tip: Always align polynomials vertically by like terms to simplify addition or subtraction.