Question

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

f(x)=x
4
−4x
3
−49x
2
+136x+420

Answer 1

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

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