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Lynna [10]
3 years ago
8

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

Mathematics
1 answer:
san4es73 [151]3 years ago
8 0

Answer:

(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

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