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

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 2

Not an option stupid

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 \(5\).

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