Question

solve : n² + 151n - 6066=0​

Answer 1

Step-by-step explanation:

The first term is, n2 its coefficient is 1 .

The middle term is, +301n its coefficient is 301 .

The last term, "the constant", is -12132

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12132 = -12132

Step-2 : Find two factors of -12132 whose sum equals the coefficient of the middle term, which is 301 .

-12132 + 1 = -12131

-6066 + 2 = -6064

-4044 + 3 = -4041

-3033 + 4 = -3029

-2022 + 6 = -2016

-1348 + 9 = -1339

-1011 + 12 = -999

-674 + 18 = -656

-337 + 36 = -301

-36 + 337 = 301 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and 337

n2 - 36n + 337n - 12132

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

n • (n-36)

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

337 • (n-36)

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

(n+337) • (n-36)

Which is the desired factorization

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