Question

What is the highest degree for the expression (3x2+4)(x5−3)−12x9−24x3x+2 ?(1 point) Responses 7 7 9 9 8 8 10

Answer 1

To find the highest degree of the expression \((3x^2 + 4)(x^5 - 3) - 12x^9 - 24x^3x + 2\), we will analyze each component.

1. **Degree of \((3x^2 + 4)(x^5 - 3)\)**:
- The highest degree term from \(3x^2\) is 2, and from \(x^5\) it is 5.
- The degree of the product will be \(2 + 5 = 7\).

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

3. **Degree of \(-24x^3x + 2\)**:
- The term \(-24x^3x\) simplifies to \(-24x^4\), which has a degree of 4.
- The constant term \(+2\) has a degree of 0.

Now we can compare the degrees from each part:
- The degree from \((3x^2 + 4)(x^5 - 3)\) is 7.
- The degree from \(-12x^9\) is 9.
- The degree from \(-24x^4 + 2\) is 4.

The highest degree among these is 9 from the \(-12x^9\) term.

Thus, the highest degree for the expression \((3x^2 + 4)(x^5 - 3) - 12x^9 - 24x^3x + 2\) is **9**.