Question

Which of the following expressions is a factor of 2x^2+9x-35 use long division to solve
A.2x-5
B.x-5
C.x-7
D.2x-7

Answer 1

To determine which of the given expressions is a factor of the polynomial \( 2x^2 + 9x - 35 \), we can use polynomial long division for each option.

### Long Division Steps:

1. **Polynomial Division of \( 2x^2 + 9x - 35 \) by \( 2x - 5 \):**

- First, divide \( 2x^2 \) by \( 2x \) to get \( x \).
- Multiply \( x \) by \( 2x - 5 \):
\[
x(2x - 5) = 2x^2 - 5x
\]
- Subtract this result from the original polynomial:
\[
(2x^2 + 9x - 35) - (2x^2 - 5x) = 14x - 35
\]
- Now, divide \( 14x \) by \( 2x \) to get \( 7 \).
- Multiply \( 7 \) by \( 2x - 5 \):
\[
7(2x - 5) = 14x - 35
\]
- Subtract this from the previous remainder:
\[
(14x - 35) - (14x - 35) = 0
\]
- Since we are left with a remainder of 0, \( 2x - 5 \) is a factor of \( 2x^2 + 9x - 35 \).

2. **Since \( 2x - 5 \) is a factor, we can conclude:**

The answer is **A. \( 2x - 5 \)**.

### Optional Checks:

You could perform the same long division process for the other options, but since we have already established that \( 2x - 5 \) is a factor, we can confirm it without checking the remaining options, although it's fine to check them for further clarity.

### Final Conclusion:
The factor of \( 2x^2 + 9x - 35 \) is:
**A. \( 2x - 5 \)**.