Factor completely. x^2−12x+35

(x-5) (x-7)

Step-by-step explanation:

x²−12x+35

note that the constant term is 35 and the x-coefficient is -12

step 1: List factors of 35 : ±1, ±5, ±7,±35

step 2: observe the factors listed and ask ourselves the following questions:

1) What 2 factors in the list , when multiplied gives the constant 35

2) What same 2 factors when added gives the x-coefficient -12

by deduction or trial and error, we can see that -5 and -7, when multiplied gives 35 and when added gives -12. Hence these become the factors.

Hence the factors are

(x-5) (x-7)