Factorise the quadratic expression below: 𝑥2−3𝑥−40x 2 −3x−40

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

The quadratic expression is: x² - 3x - 40

Step 1: Identify the coefficients of the quadratic expression. Here, a = 1 (coefficient of x²), b = -3 (coefficient of x), and c = -40 (constant term).

Step 2: We need to find two numbers that multiply to give ac (which is -40 in this case) and add up to give b (which is -3 in this case).

The numbers that satisfy these conditions are -8 and 5 because (-8) * 5 = -40 and -8 + 5 = -3.

Step 3: Rewrite the middle term of the quadratic expression as the sum of the products of x and the two numbers we found. The expression becomes:

x² - 8x + 5x - 40

Step 4: Factor by grouping. The first two terms have a common factor of x, and the last two terms have a common factor of 5. So, we can rewrite the expression as:

x(x - 8) + 5(x - 8)

Step 5: Notice that (x - 8) is a common factor of both terms. So, we can factor it out to get the final factorised form of the quadratic expression:

(x - 8)(x + 5)

So, the factorised form of the quadratic expression x² - 3x - 40 is (x - 8)(x + 5).