What is the sum of the polynomials `6a ^(2) -17a -9 and -5a ^(2) + 8a -2` ?

Options

A. `a ^(2) -9a -11`
B. `a ^(2)- 25a -7`
C. `11a ^(2) -9a-11`
D. `11a ^(2) -25a-7`

Answer

To find the sum of the polynomials \(6a^2 - 17a - 9\) and \(-5a^2 + 8a - 2\), we will follow these steps:

### Step 1: Write down the polynomials
We have the two polynomials:
1. \(6a^2 - 17a - 9\)
2. \(-5a^2 + 8a - 2\)

### Step 2: Group like terms
We will group the terms based on their degrees (powers of \(a\)):
- The \(a^2\) terms: \(6a^2\) and \(-5a^2\)
- The \(a\) terms: \(-17a\) and \(8a\)
- The constant terms: \(-9\) and \(-2\)

### Step 3: Add the \(a^2\) terms
Now, we add the \(a^2\) terms:
\[ 6a^2 + (-5a^2) = 6a^2 - 5a^2 = 1a^2 \text{ or simply } a^2 \]

### Step 4: Add the \(a\) terms
Next, we add the \(a\) terms:
\[ -17a + 8a = -17a + 8a = -9a \]

### Step 5: Add the constant terms
Finally, we add the constant terms:
\[ -9 + (-2) = -9 - 2 = -11 \]

### Step 6: Combine all the results
Now, we combine all the results from the previous steps:
\[ a^2 - 9a - 11 \]

Thus, the sum of the polynomials \(6a^2 - 17a - 9\) and \(-5a^2 + 8a - 2\) is:
\[ \boxed{a^2 - 9a - 11} \]

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