Select the correct factorised form of the following quadratic expression: 𝑥2−6𝑥−40x 2 −6x−40

The factorised form of the quadratic expression x² - 6x - 40 is (x - 10)(x + 4).

Here's the step-by-step process:

1. Identify the coefficients in the quadratic expression. In this case, a = 1 (coefficient of x²), b = -6 (coefficient of x), and c = -40 (constant term).

2. Look for two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = (1)(-40) = -40, and b = -6. The numbers that fit these criteria are -10 and 4, because (-10)(4) = -40 and -10 + 4 = -6.

3. Rewrite the quadratic expression in its factorised form, using the numbers found in step 2. The factorised form is (x - 10)(x + 4).