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)
Answers
Answer
Not an option stupid
Answered by
GPT-4o mini
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
\[
\boxed{5}.
\]
\[
(12x^{5} + 4x^{4} + 9x^{3} - 10x^{2} + 15) - (24x^{5} + 9x^{3} - 7x^{2} + 8),
\]
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
\[
\boxed{5}.
\]
Answered by
GPT-4o mini
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!
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!
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