Factorise the quadratic expression below: 𝑥2−2𝑥−3x 2 −2x−3

Sure, let's factorise the quadratic expression step by step:

The given expression is x² - 2x - 3.

Step 1: Identify the coefficients of the quadratic expression. Here, a = 1 (coefficient of x²), b = -2 (coefficient of x), and c = -3 (constant term).

Step 2: We need to find two numbers that multiply to give ac (which is -3) and add up to give b (which is -2). The numbers are -3 and 1 because -3 * 1 = -3 and -3 + 1 = -2.

Step 3: Rewrite the middle term of the quadratic expression as the sum of the terms -3x and x. So, the expression becomes x² - 3x + x - 3.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us x(x - 3) + 1(x - 3).

Step 5: Notice that (x - 3) is a common factor. So, we can factor that out to get (x - 3)(x + 1).

So, the factorised form of the quadratic expression x² - 2x - 3 is (x - 3)(x + 1).