Factorise :y²-5y-24

y²-5y-24
= y²-8y+3y-24
= y(y-8) + 3(y-8)
= (y-8) (y+3)

Detailed explanation:

Factoring  y²-5y-24 

The first term is,  y²  its coefficient is  1 .
The middle term is,  -5y  its coefficient is  -5 .
The last term, "the constant", is  -24 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3 
                     y² - 8y + 3y - 24

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (y-8)
              Add up the last 2 terms, pulling out common factors :
                    3 • (y-8)
Step-5 : Add up the four terms of step 4 :
                    (y+3)  •  (y-8)