For what value of k will x - 4 be a factor of x ^2 + kx - 52? Show how you arrived at your answer.

Remember GM....if x - 4 is a factor then 4 is a root

This is where the Remainder Theorem comes in handy

So....if  4 is a root....then  putting 4 into the function will return 0....so....

(4)^2 +  k(4) - 52 = 0   simplify

16  + 4k   - 52 = 0

-36 + 4k = 0      add 36 to both sides

4k =  36           divide both sides by 4

k = 9

So....we have    x^2 + 9x - 52

Notice that this factors  as  ( x - 4) (x + 13)

Note that (x - 4) is a factor