Is `3x^(2) - 8x - 15` factorisable ? If yes, factorise it.

Answer

To determine whether the quadratic expression \(3x^2 - 8x - 15\) is factorable, we will follow these steps:

### Step 1: Identify coefficients
The given quadratic expression is in the form \(ax^2 + bx + c\). Here, we identify:
- \(a = 3\)
- \(b = -8\)
- \(c = -15\)

### Step 2: Calculate the discriminant
The discriminant \(D\) is calculated using the formula:
\[ D = b^2 - 4ac \]
Substituting the values of \(a\), \(b\), and \(c\):
\[ D = (-8)^2 - 4 \cdot 3 \cdot (-15) \]
Calculating each part:
\[ D = 64 - 4 \cdot 3 \cdot (-15) \]
\[ D = 64 - (-180) \]
\[ D = 64 + 180 \]
\[ D = 244 \]

### Step 3: Check if the discriminant is a perfect square
Now we need to check if \(244\) is a perfect square. The square root of \(244\) is approximately \(15.62\), which is not an integer. Therefore, \(244\) is not a perfect square.

### Step 4: Conclusion
Since the discriminant \(D\) is not a perfect square, the quadratic expression \(3x^2 - 8x - 15\) is not factorable.

### Final Answer
The expression \(3x^2 - 8x - 15\) is not factorable.

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