Factorise the quadratic expression below: 𝑥2+𝑥−72x 2 +x−72

Sure, here are the steps to factorise the quadratic expression x^2 + x - 72:

1. First, we need to find two numbers that multiply to -72 (the constant term) and add to 1 (the coefficient of the x term). Those numbers are 9 and -8 because 9 * -8 = -72 and 9 + -8 = 1.

2. Rewrite the middle term of the quadratic expression as the sum of the terms 9x and -8x. This gives us x^2 + 9x - 8x - 72.

3. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us (x^2 + 9x) - (8x + 72).

4. Factor out the greatest common factor from each group. From the first group, we can factor out an x, and from the second group, we can factor out an -8. This gives us x(x + 9) - 8(x + 9).

5. Notice that (x + 9) is a common factor of both terms. We can factor out (x + 9), which gives us (x + 9)(x - 8).

So, the factorised form of the quadratic expression x^2 + x - 72 is (x + 9)(x - 8).