F(x)=x^4-4x^3-49x^2+136x+420
f(x)=x
4
−4x
3
−49x
2
+136x+420

(x+6)(x+2)(x-5)(x-7)

Step-by-step explanation:

step 1: x4)-(4•(x3)))-72x2)+136x)+420

step 2: x4) -  22x3) -  72x2) +  136x) +  420

step 3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  6

                    x2 + 2x + 6x + 12

step 4: Add up the first 2 terms, pulling out like factors :

                   x • (x+2)

             Add up the last 2 terms, pulling out common factors :

                   6 • (x+2)

step 5: Add up the four terms of step 4 :

                   (x+6)  •  (x+2)

            Which is the desired factorization