Factorise x2+4x−5 completely.

To factorise the quadratic equation x^2 + 4x - 5, we need to find two numbers that add up to 4 (the coefficient of x) and multiply to -5 (the constant term).

The two numbers that satisfy these conditions are 5 and -1 because:

5 + (-1) = 4 5 * (-1) = -5

Therefore, we can write the equation as:

x^2 + 5x - x - 5

Now, we can factor by grouping:

x(x + 5) - 1(x + 5)

Finally, we can factor out the common binomial term to get the completely factorised form of the equation:

(x - 1)(x + 5)

So, x^2 + 4x - 5 = (x - 1)(x + 5) when completely factorised.