Use the same technique as in (4 and 5) above to factorise \( x^{2}+3 x-4 \). Show all the Steps. \( \begin{array}{l}\text { Use the same technique as in (4 and 5) above to factorise the following } \\ \text { Show all the Steps. } \\ 7.1\end{array} x^{2}-x-6 \).

To factor the quadratic expression \( x^{2}+3x-4 \), we will use the method of finding two numbers that multiply to the constant term (-4) and add to the coefficient of the linear term (+3). **Step 1:** Identify the numbers. We need two numbers that multiply to \(-4\) and add to \(3\). The numbers \(4\) and \(-1\) satisfy this because: \[ 4 \times (-1) = -4 \quad \text{and} \quad 4 + (-1) = 3. \] **Step 2:** Rewrite the expression using the identified numbers. Now, we can rewrite the quadratic expression: \[ x^2 + 4x - 1x - 4. \] **Step 3:** Group the terms. Next, group the terms into two pairs: \[ (x^2 + 4x) + (-1x - 4). \] **Step 4:** Factor by grouping. Factoring each group, we have: \[ x(x + 4) - 1(x + 4). \] Now, factor out the common binomial \((x + 4)\): \[ (x + 4)(x - 1). \] Thus, the factorization of \( x^{2}+3x-4 \) is: \[ (x + 4)(x - 1). \] Now, let's factor the quadratic expression \( x^{2}-x-6 \) using a similar approach. **Step 1:** Identify the numbers. We need two numbers that multiply to \(-6\) and add to \(-1\). These numbers are \(2\) and \(-3\) because: \[ 2 \times (-3) = -6 \quad \text{and} \quad 2 + (-3) = -1. \] **Step 2:** Rewrite the expression with the identified numbers. Now, we can rewrite the expression: \[ x^2 + 2x - 3x - 6. \] **Step 3:** Group the terms. Next, group the terms into two pairs: \[ (x^2 + 2x) + (-3x - 6). \] **Step 4:** Factor by grouping. Factoring each group, we have: \[ x(x + 2) - 3(x + 2). \] Now, factor out the common binomial \((x + 2)\): \[ (x + 2)(x - 3). \] Thus, the factorization of \( x^{2}-x-6 \) is: \[ (x + 2)(x - 3). \]