Factorise:
`6p^(2) + 11p -10`

Answer

To factorise the expression \(6p^2 + 11p - 10\), we will follow these steps:

### Step 1: Identify the coefficients
The given expression is \(6p^2 + 11p - 10\).
- Coefficient of \(p^2\) (a) = 6
- Coefficient of \(p\) (b) = 11
- Constant term (c) = -10

### Step 2: Multiply the coefficient of \(p^2\) and the constant term
We need to multiply \(a\) and \(c\):
\[ a \cdot c = 6 \cdot (-10) = -60 \]

### Step 3: Find two numbers that multiply to -60 and add to 11
We need to find two numbers that multiply to \(-60\) and add up to \(11\). The numbers that satisfy this condition are \(15\) and \(-4\) because:
\[ 15 \cdot (-4) = -60 \quad \text{and} \quad 15 + (-4) = 11 \]

### Step 4: Rewrite the middle term using the two numbers
Now, we can rewrite the expression by splitting the middle term \(11p\) into \(15p - 4p\):
\[ 6p^2 + 15p - 4p - 10 \]

### Step 5: Group the terms
Next, we will group the terms:
\[ (6p^2 + 15p) + (-4p - 10) \]

### Step 6: Factor out the common factors from each group
Now, factor out the common factors from each group:
\[ 3p(2p + 5) - 2(2p + 5) \]

### Step 7: Factor out the common binomial factor
Now we can see that \((2p + 5)\) is a common factor:
\[ (3p - 2)(2p + 5) \]

### Final Factorised Form
Thus, the factorised form of the expression \(6p^2 + 11p - 10\) is:
\[ (3p - 2)(2p + 5) \]

---