Factorise 4p2−11p−15 completely.

Sure, here are the steps to factorise the quadratic equation 4p^2 - 11p - 15:

Step 1: Multiply the coefficient of p^2 (which is 4) and the constant term (which is -15). The result is -60.

Step 2: Look for two numbers that multiply to -60 and add to -11 (the coefficient of p). The numbers are -15 and 4.

Step 3: Rewrite the middle term of the equation as the sum of the terms -15p and 4p. The equation becomes 4p^2 - 15p + 4p - 15.

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 4p(p - 15/4) + 1(p - 15/4).

Step 5: Notice that (p - 15/4) is a common factor. Factor out (p - 15/4) to get (p - 15/4)(4p + 1).

So, the factorised form of 4p^2 - 11p - 15 is (p - 15/4)(4p + 1).