Factorise:
`3x^(2) + 10 x + 8`

Answer

To factorise the expression \(3x^2 + 10x + 8\), we will follow these steps:

### Step 1: Identify the coefficients
The coefficients of the quadratic expression are:
- Coefficient of \(x^2\) (a) = 3
- Coefficient of \(x\) (b) = 10
- Constant term (c) = 8

### Step 2: Multiply the coefficient of \(x^2\) by the constant term
We need to multiply \(a\) and \(c\):
\[ 3 \times 8 = 24 \]

### Step 3: Find two numbers that multiply to 24 and add to 10
We are looking for two numbers that multiply to 24 and add up to 10. The numbers are 6 and 4:
\[ 6 \times 4 = 24 \quad \text{and} \quad 6 + 4 = 10 \]

### Step 4: Rewrite the middle term
We can rewrite the expression \(3x^2 + 10x + 8\) by splitting the middle term using the numbers found:
\[ 3x^2 + 6x + 4x + 8 \]

### Step 5: Group the terms
Now, we will group the terms:
\[ (3x^2 + 6x) + (4x + 8) \]

### Step 6: Factor out the common factors from each group
From the first group \(3x^2 + 6x\), we can factor out \(3x\):
\[ 3x(x + 2) \]
From the second group \(4x + 8\), we can factor out \(4\):
\[ 4(x + 2) \]

### Step 7: Combine the factored terms
Now we have:
\[ 3x(x + 2) + 4(x + 2) \]
We can factor out the common binomial \((x + 2)\):
\[ (x + 2)(3x + 4) \]

### Final Answer
Thus, the factorised form of \(3x^2 + 10x + 8\) is:
\[ (3x + 4)(x + 2) \]

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