To add the two polynomials, we combine like terms. The two polynomials are:

1. $(5x^2 - 7x + 4)$
2. $(2x^2 + 3x + 5)$

Step-by-step addition:

• Combine the $x^2$ terms: $5x^2 + 2x^2 = 7x^2$
• Combine the $x$ terms: $-7x + 3x = -4x$
• Combine the constant terms: $4 + 5 = 9$

Final result:

$7x^2 - 4x + 9$

So, the sum of the two polynomials is $7x^2 - 4x + 9$.

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Would you like more details or have any questions about this process?

Here are 5 related questions for further practice:

1. What is the difference between the two polynomials $(5x^2 - 7x + 4)$ and $(2x^2 + 3x + 5)$?
2. How do you add polynomials with more terms, such as $3x^3 - 4x^2 + 2x + 6$ and $5x^3 + 2x^2 - x + 1$?
3. Can you explain the concept of "like terms" in polynomials with an example?
4. How would you subtract polynomials like $(6x^2 + 4x + 7)$ from $(2x^2 - 3x + 5)$?
5. How do you multiply two polynomials, such as $(3x + 2)$ and $(x^2 - 4)$?

Tip: When adding or subtracting polynomials, always group like terms together based on their degree (highest power of the variable).