Question

What is the highest degree for the expression (12x^(5)+4x^(4)+9x^(3)-10x^(2)+15)-(24x^(5+)9x^(3)-7x^(2)+8)

Answer 1

Not an option stupid

Answer 2

To determine the highest degree of the expression

\[
(12x^{5} + 4x^{4} + 9x^{3} - 10x^{2} + 15) - (24x^{5} + 9x^{3} - 7x^{2} + 8),
\]

we need to simplify it first.

1. Combine the like terms inside the parentheses. The original expression can be rewritten as:

\[
12x^{5} + 4x^{4} + 9x^{3} - 10x^{2} + 15 - 24x^{5} - 9x^{3} + 7x^{2} - 8.
\]

2. Now, distribute the negative sign through the second parenthesis:

\[
12x^{5} - 24x^{5} + 4x^{4} + 9x^{3} - 9x^{3} - 10x^{2} + 7x^{2} + 15 - 8.
\]

3. Combine the like terms:

- For \(x^{5}\): \(12x^{5} - 24x^{5} = -12x^{5}\).
- For \(x^{4}\): \(4x^{4}\) (no other \(x^4\) terms).
- For \(x^{3}\): \(9x^{3} - 9x^{3} = 0\).
- For \(x^{2}\): \(-10x^{2} + 7x^{2} = -3x^{2}\).
- For the constant terms: \(15 - 8 = 7\).

Putting it all together, we get:

\[
-12x^{5} + 4x^{4} - 3x^{2} + 7.
\]

4. Now, identify the highest degree term. The highest degree term in this expression is \(-12x^{5}\), which is of degree \(5\).

Thus, the highest degree for the given expression is

\[
\boxed{5}.
\]

Answer 3

I apologize for any confusion! Let's carefully go through the expression again step by step.

The expression to simplify is:

\[
(12x^{5} + 4x^{4} + 9x^{3} - 10x^{2} + 15) - (24x^{5} + 9x^{3} - 7x^{2} + 8).
\]

### Step 1: Distributing the negative sign

We can distribute the negative sign across the second parentheses:

\[
12x^{5} + 4x^{4} + 9x^{3} - 10x^{2} + 15 - 24x^{5} - 9x^{3} + 7x^{2} - 8.
\]

### Step 2: Combine like terms

Now we'll combine the coefficients of like terms:

- **For \(x^{5}\)**:
\[
12x^{5} - 24x^{5} = -12x^{5}
\]

- **For \(x^{4}\)**:
\[
4x^{4}
\]

- **For \(x^{3}\)**:
\[
9x^{3} - 9x^{3} = 0
\]

- **For \(x^{2}\)**:
\[
-10x^{2} + 7x^{2} = -3x^{2}
\]

- **For constants**:
\[
15 - 8 = 7
\]

### Final Expression

After combining all the terms, we have:

\[
-12x^{5} + 4x^{4} - 3x^{2} + 7.
\]

### Step 3: Determine the highest degree

The highest degree in this expression is from the term \(-12x^{5}\), which has a degree of \(5\).

If this result is not what you expected, please provide clarification or let me know the options available, and I would be happy to assist further!