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

Answer

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

### Step 1: Identify Like Terms
The expression consists of several terms: \(4k\), \(-3k^2\), \(-5k\), and \(6\). The like terms are those that contain the same variable raised to the same power.

**Like terms:**
- The terms \(4k\) and \(-5k\) are like terms (both are linear terms in \(k\)).
- The term \(-3k^2\) is a quadratic term.
- The term \(6\) is a constant.

### Step 2: Combine Like Terms
Now, we will combine the like terms.

1. Combine \(4k\) and \(-5k\):
\[ 4k - 5k = -1k \text{ or } -k \]

So, we can rewrite the expression as:
\[ -3k^2 - k + 6 \]

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

### Final Answer:
Thus, the simplified form of the expression \(4k - 3k^2 - 5k + 6\) is:
\[ -3k^2 - k + 6 \]

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