Factorise : z²-7z-30

Factoring  z²-7z-30 

The first term is,  z²  its coefficient is  1 .
The middle term is,  -7z  its coefficient is  -7 .
The last term, "the constant", is  -30 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -30 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  3 
                     z² - 10z + 3z - 30

Step-4 : Add up the first 2 terms, pulling out like factors :
                    z • (z-10)
              Add up the last 2 terms, pulling out common factors :
                    3 • (z-10)
Step-5 : Add up the four terms of step 4 :
                    (z+3)  •  (z-10)

Hence, z2−7z−30=(z−10)(z+3).