Question

What is the highest degree for the expression (3x2+4)(x5−3)−12x9−24x3x+2 ?(1 point) Responses 9 9 8 8 1010 7

Answer 1

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

1. The highest degree term from \( (3x^2 + 4)(x^5 - 3) \) can be found by multiplying the highest degree terms of each factor:
- The highest degree term of \( 3x^2 \) is \( 2 \).
- The highest degree term of \( x^5 \) is \( 5 \).
- The degree of the product is \( 2 + 5 = 7 \).

However, we also consider the lower degree terms:
- From \( 3x^2 \times (-3) \): degree \( 2 \).
- From \( 4 \times x^5 \): degree \( 5 \).
- From \( 4 \times (-3) \): degree \( 0 \).

The maximum degree in \( (3x^2 + 4)(x^5 - 3) \) is \( 7 \).

2. Now, we consider the term \( -12x^9 \):
- The degree is \( 9 \).

3. Next, we have \( -24x^3x + 2 \):
- \( -24x^4 \) has a degree of \( 4 \).
- The constant \( 2 \) has a degree of \( 0 \).

Now we can summarize:

- From \( (3x^2 + 4)(x^5 - 3) \): degree \( 7 \)
- From \( -12x^9 \): degree \( 9 \)
- From \( -24x^4 + 2 \): degree \( 4 \)

The overall highest degree in the expression is from \( -12x^9 \), which is \( 9 \).

Thus, the highest degree for the expression is **9**.