Question

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

7
7

1010

8
8

9

Answer 1

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

1. **Finding the degree of \( (3x^2 + 4)(x^5 - 3) \)**:
- The degree of \( 3x^2 + 4 \) is 2 (from the term \( 3x^2 \)).
- The degree of \( x^5 - 3 \) is 5 (from the term \( x^5 \)).
- When multiplying these two polynomials, the degrees add, so the degree of \( (3x^2 + 4)(x^5 - 3) \) is \( 2 + 5 = 7 \).

2. **Finding the degree of \( -12x^9 \)**:
- The degree is 9.

3. **Finding the degree of \( -24x^3 \)**:
- The degree is 3.

4. **Finding the degree of \( +2 \)**:
- The degree is 0.

Now, we can put it all together:

- The highest degree from \( (3x^2 + 4)(x^5 - 3) \) is 7.
- The highest degree from \( -12x^9 \) is 9.
- The others have lower degrees.

Thus, the highest degree overall in the entire expression is from the term \( -12x^9 \), which is **9**.

So the answer is **9**.