Question

What is the highest degree for the expression (3x2+4)(x5−3)−12x9−24x3x+2?(1 point)
Responses

9
9

8
8

10
10

7
7

Answer 1

To determine the highest degree of the expression \((3x^2 + 4)(x^5 - 3) - 12x^9 - 24x^3 x + 2\), we first need to find the degree of each part of the expression.

1. **For the product \((3x^2 + 4)(x^5 - 3)\)**:
- The degree of \(3x^2\) is 2.
- The degree of \(x^5\) is 5.
- When multiplying, the degrees add, so the degree of \((3x^2 + 4)(x^5 - 3)\) is \(2 + 5 = 7\).

2. **Next, consider \(-12x^9\)**:
- This term has a degree of 9.

3. **Now, look at \(-24x^3x\)**:
- This can be simplified to \(-24x^4\), which has a degree of 4.

4. **Finally, the constant term \(+2\)**:
- This term has a degree of 0.

Now we compile the degrees from each part:
- From \((3x^2 + 4)(x^5 - 3)\): degree 7
- From \(-12x^9\): degree 9
- From \(-24x^4\): degree 4
- From \(+2\): degree 0

The highest degree among these terms is \(\text{degree } 9\) from \(-12x^9\).

Thus, the highest degree for the expression is:

**9**