Factor p squared minus 6p plus five equals zero

Question

^p2-6p+5=0

Answer 1

Kelsey:

 

This is something you should be doing yourself.  But here is a hint.

 

(x-a)(x-b)=x2-(a+b)x+ab

 

Compare this with

 

x2-6x+5

 

Note that a and b are factors of 5.

Answer 2

Let’s review the steps in factoring the equation Ax² + Bx + C = 0

Divide everything by A so that the coefficient of x² is 1:
                 x² + (B/A)x + C/A = 0
                 (x + D)(x + E) = 0      (let -D and -E be the “roots;” the values of x that make f(x)=0)
                  x² + (E + D)x + DE = 0          (expand using FOIL)
         This means that (B/A)=(E+D)  and that  (C/A)=(DE).

         That’s why we look for factors of C, because we expect D and E to be integer factors.

Now, if A=1 already, this is super-easy.  What two numbers multiplied together to give 5 and added together to give -6?   Well, the negative sign makes this a little bit hard, but you can do it !