Simplify : `4k - 3k^(2)-5k +6`

Options

A. `k^(2) + k + 4`
B. ` -3k^(2) - k +6`
C. `3k^(2) - 9k + 4`
D. `3k^(2) - 9k - 4`

Answer

To simplify the expression \(4k - 3k^2 - 5k + 6\), we will follow these steps:

### Step 1: Identify Like Terms
First, we need to identify the like terms in the expression. Like terms are terms that have the same variable raised to the same power.

In the expression \(4k - 3k^2 - 5k + 6\):
- The terms \(4k\) and \(-5k\) are like terms (both have the variable \(k\)).
- The term \(-3k^2\) is not a like term with \(4k\) or \(-5k\) (it has \(k^2\)).
- The constant term is \(6\), which is also not a like term with the others.

### Step 2: Combine Like Terms
Now, we will combine the like terms \(4k\) and \(-5k\):
\[ 4k - 5k = (4 - 5)k = -1k = -k \]

### Step 3: Rewrite the Expression
After combining the like terms, we can rewrite the expression:
\[ -3k^2 - k + 6 \]

### Step 4: Final Expression
The simplified expression is:
\[ -3k^2 - k + 6 \]

### Summary of Steps:
1. Identify like terms: \(4k\) and \(-5k\).
2. Combine like terms: \(4k - 5k = -k\).
3. Rewrite the expression: \(-3k^2 - k + 6\).
4. Present the final simplified expression: \(-3k^2 - k + 6\).

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