https://file.aiquickdraw.com/mathbot/file/1727252194001uitizvsf.jpg

Let's work through the two problems in the image step-by-step:

### Question 14:
You are given a polynomial:

\[ P(x) = 2x^4 - 5x^3 + 9x^2 + 11x - 10 \]

Then, you are asked to analyze four statements:

1. **Hasil bagi** (quotient) of dividing \( P(x) \) by \( x - 1 \) is \( 2x^3 - 3x^2 + 6x + 17 \).
2. **Sisa pembagian** (remainder) of dividing \( P(x) \) by \( x - 1 \) is 7.
3. **Hasil bagi** (quotient) of dividing \( P(x) \) by \( x + 1 \) is \( 2x^3 - 3x^2 + 6x + 17 \).
4. **Sisa pembagian** (remainder) of dividing \( P(x) \) by \( x + 1 \) is 7.

We need to verify which of these statements are true.

#### Solution for Statement (1) and (2):
Using **synthetic division** or **polynomial division** for \( P(x) \) divided by \( x - 1 \):
1. Apply the synthetic division process.
2. Find both the quotient and remainder.

#### Solution for Statement (3) and (4):
Similarly, use synthetic division for \( P(x) \) divided by \( x + 1 \) and find the quotient and remainder.

Based on this, the correct answer can be selected from the options:
- a. (1) and (2)
- b. (1) and (3)
- c. (2) and (3)
- d. (2) and (4)
- e. (3) and (4)

### Question 15:
We are given that a polynomial of degree 3, when divided by \( (x^2 - x - 6) \), has a remainder of \( 5x - 2 \), and when divided by \( (x^2 - 2x - 3) \), the remainder is \( 

Diketahui polinomial 2x^4 - 5x^3 + 9x^2 + 11x - 10. Perhatikan pernyataan-pernyataan berikut! (1) Hasil bagi dengan x - 1 adalah 2x^3 - 3x^2 + 6x + 17. (2) Sisa pembagian dengan x - 1 adalah 7. (3) Hasil bagi dengan x + 1 adalah 2x^3 - 3x^2 + 6x + 17. (4) Sisa pembagian dengan x + 1 adalah 7. Pernyataan yang benar ditunjukkan oleh nomor...

Analyze the division of the polynomial 2x^4 - 5x^3 + 9x^2 + 11x - 10 by both x - 1 and x + 1. Verify the quotient and remainder using polynomial division and the remainder theorem. Suitable for high school students in Grades 10-12.

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