Read each item carefully and write the CAPITAL letter that corresponds to your answer. Write your answer in a separate sheet of paper.

1. Evaluate P(x) = 7x ^ 3 + 6x ^ 4 - 8x ^ 6 + 6x + 11 at x = 0 
A. 11
B.8
C.7
D. 6

2. What is f(3) if f(x)=x² - 3x + 2x⁴ +1?
 A.91
B. 10
C.30
D. 3

3. If P(x) = x ^ 4 - 4x ^ 2 + 3x + 2 then P(2)?
A.2
B.8
 C. 14
D. 20

4. What is B(x) + S(x) given that B(x) = 7x ^ 2 - 5x + 100 and S(x) = 20x ^ 2 + 60x + 200?

B. 27x ^ 2 - 65x + 200
 D. 17x ^ 2 - 45x + 300
A.27x ^ 2 + 55x + 300 
C. 17x ^ 2 + 45x + 300

5. Write a polynomial to express the total value, T(x), of (x + 4) 20-peso bills, (x-3) 50-peso bills, (x + 5) 100-peso bills, and (x-2) bills.

A. T(x)= 20(x+4)+50(x-3)+100(x+5) +200(x-2)
B. T(x) = 20(x + 4) - 50(x - 3) - 100(x + 5) - 200(x - 2) 
C. T(x)= 20(x+4)x50(x-3) x 100(x + 5) x 200(x-2)
D. T(x) = 20(x + 4) + 50(x - 3) + 100(x + 5) + 200(x - 2)

Let's evaluate each item carefully.

### 1. Evaluate \( P(x) = 7x^3 + 6x^4 - 8x^6 + 6x + 11 \) at \( x = 0 \).
When \( x = 0 \), all terms with \( x \) become zero:
\[
P(0) = 7(0)^3 + 6(0)^4 - 8(0)^6 + 6(0) + 11 = 11
\]
The correct answer is **A. 11**.

---

### 2. What is \( f(3) \) if \( f(x) = x^2 - 3x + 2x^4 + 1 \)?
Substitute \( x = 3 \) into the function:
\[
f(3) = 3^2 - 3(3) + 2(3)^4 + 1 = 9 - 9 + 2(81) + 1 = 0 + 162 + 1 = 163
\]
It looks like there’s no option with 163, so this might need a correction. But based on the expression, it evaluates to **163**, which doesn't match the provided options.

---

### 3. If \( P(x) = x^4 - 4x^2 + 3x + 2 \), then find \( P(2) \):
\[
P(2) = 2^4 - 4(2^2) + 3(2) + 2 = 16 - 4(4) + 6 + 2 = 16 - 16 + 6 + 2 = 8
\]
The correct answer is **B. 8**.

---

### 4. What is \( B(x) + S(x) \) given that \( B(x) = 7x^2 - 5x + 100 \) and \( S(x) = 20x^2 + 60x + 200 \)?
Add the two polynomials:
\[
B(x) + S(x) = (7x^2 - 5x + 100) + (20x^2 + 60x + 200) = 27x^2 + 55x + 300
\]
The correct answer is **A. 27x^2 + 55x + 300**.

---

### 5. Write a polynomial to express the total value, \( T(x) \), of the given bills.
The total value is the sum of all bills:
\[
T(x) = 20(x + 4) + 50(x - 3) + 100(x + 5) + 200(x - 2)
\]
Simplify the expression:
\[
T(x) = 20x + 80 + 50x - 150 + 100x + 500 + 200x - 400 = 370x + 30
\]
None of the options matches this result exactly, but **option D** seems closest in form as a sum of terms.

---

### Summary of Answers:
1. **A**
2. **(none of the provided options fit)**
3. **B**
4. **A**
5. **D**

---

Do you want further details or explanations on any of the items?

Here are 5 related questions to think about:
1. What happens when you evaluate \( P(x) = 7x^3 + 6x^4 - 8x^6 + 6x + 11 \) for a different value of \( x \), like \( x = 1 \)?
2. Can you simplify a different function, say \( g(x) = 2x^5 + 3x^2 + 4x - 7 \), at \( x = 2 \)?
3. What are the steps to factor the polynomial \( x^4 - 4x^2 + 3x + 2 \)?
4. How do you combine two polynomials with opposite signs, like \( B(x) - S(x) \)?
5. Can you create a similar bill problem for a different currency?

**Tip**: When adding or subtracting polynomials, group like terms and simplify step by step to avoid errors.

Read each item carefully and write the CAPITAL letter that corresponds to your answer. Write your answer in a separate sheet of paper.

1. Evaluate P(x) = 7x^3 + 6x^4 - 8x^6 + 6x + 11 at x = 0
A. 11
B. 8
C. 7
D. 6

2. What is f(3) if f(x) = x² - 3x + 2x⁴ + 1?
A. 91
B. 10
C. 30
D. 3

3. If P(x) = x^4 - 4x^2 + 3x + 2 then P(2)?
A. 2
B. 8
C. 14
D. 20

4. What is B(x) + S(x) given that B(x) = 7x^2 - 5x + 100 and S(x) = 20x^2 + 60x + 200?
A. 27x^2 + 55x + 300
B. 27x^2 - 65x + 200
C. 17x^2 + 45x + 300
D. 17x^2 - 45x + 300

5. Write a polynomial to express the total value, T(x), of (x + 4) 20-peso bills, (x - 3) 50-peso bills, (x + 5) 100-peso bills, and (x - 2) 200-peso bills.
A. T(x) = 20(x + 4) + 50(x - 3) + 100(x + 5) + 200(x - 2)
B. T(x) = 20(x + 4) - 50(x - 3) - 100(x + 5) - 200(x - 2)
C. T(x) = 20(x + 4) * 50(x - 3) * 100(x + 5) * 200(x - 2)
D. T(x) = 20(x + 4) + 50(x - 3) + 100(x + 5) + 200(x - 2)

Learn how to evaluate polynomial functions and add polynomials through a detailed step-by-step solution to this problem set. The questions cover polynomial expressions, function evaluation, and polynomial addition. Suitable for students in Grades 9-11.

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