Select the correct factorised form of the following quadratic expression: 𝑥2+4𝑥−32x 2 +4x−32

The factorised form of the quadratic expression x^2 + 4x - 32 is (x - 4)(x + 8).

Here's the step-by-step process:

1. Identify the coefficients in the quadratic expression. In this case, a = 1, b = 4, and c = -32.

2. Look for two numbers that multiply to give ac (which is -32) and add to give b (which is 4). The numbers that satisfy these conditions are -4 and 8.

3. Rewrite the middle term of the quadratic expression as the sum of the terms 8x and -4x. This gives us x^2 + 8x - 4x - 32.

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 + 8) - 4(x + 8).

5. Notice that (x + 8) is a common factor. Factor out this term to get (x - 4)(x + 8).

So, the factorised form of the quadratic expression x^2 + 4x - 32 is (x - 4)(x + 8).