https://file.aiquickdraw.com/mathbot/file/1726006541996s7w7jxez.jpg

In the image, I can see the following polynomial functions and expressions written:

1. **\( P(x) = 5x^2 + 13x - 40 \)**
2. **\( Q(x) = 10x^2 + 10x + 75 \)**
3. **\( T(x) = 2x^3 + 10x^2 + 4x - 5 \)**

Additionally, there are some algebraic operations indicated with functions like:
- \( (T + S)(x) \)
- \( (S - R)(x) \)
- \( T - S \)
- \( (P + S)(x) \)
- \( (T - S)(x) \)

It seems that you are working on polynomial addition, subtraction, and function operations. Let me know if you need help solving or simplifying any of these expressions or equations!

Would you like detailed steps on how to perform any of these operations, or do you have any specific questions regarding this problem?

Here are five related questions to expand on this:

1. How do you perform addition and subtraction of polynomial functions?
2. How can we factor the given polynomial functions, if possible?
3. Can you determine the roots of the polynomial \( P(x) = 5x^2 + 13x - 40 \)?
4. What is the degree of the polynomial \( T(x) = 2x^3 + 10x^2 + 4x - 5 \)?
5. How do you compute the derivative of the polynomial \( Q(x) = 10x^2 + 10x + 75 \)?

**Tip:** Always ensure to arrange polynomials in standard form (from highest to lowest degree) before performing addition or subtraction to avoid errors in the computation.

Given a set of polynomial functions P(x), Q(x), and T(x) with corresponding algebraic operations, simplify or perform the operations (P + S)(x), (S - R)(x), T - S, and others.

Explore polynomial operations including addition, subtraction, and function operations. Simplify expressions like (T + S)(x) and (S - R)(x) for polynomials like P(x) = 5x^2 + 13x - 40. Suitable for students in Grades 10-12.

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