Question

factorize m^3-9n^2+26n-24​

Answer 1

Given :- factorise :- n^3-9n^2+26n-24 ?

Solution :-

→ p(n) = n³ - 9n² + 26n - 24

checking, n = 1,

→ p(1) = (1)³ - 9(1)² + 26*1 - 24 = 1 - 9 + 26 - 24 = (-6) ≠ 0

checking , n = 2

→ p(2) = (2)³ - 9(2)² + 26*2 - 24 = 8 - 36 + 52 - 24 = 60 - 60 = 0 .

so, (n - 2) is factor of given polynomial .

now, dividing p(n) by (n - 2) we get,

n - 2 ) n³ - 9n² + 26n - 24 ( n² - 7n + 12

-n³ - 2n²

-7n² + 26n

-7n² + 14n

12n - 24

-12n - 24

0

then,

→ p(n) = (n - 2)(n² - 7n + 12)

→ p(n) = (n - 2)(n² - 4n - 3n + 12)

→ p(n) = (n - 2)[n(n - 4) - 3(n - 4)]

→ p(n) = (n - 2)[(n - 4)(n - 3)]

therefore,

→ n³ - 9n² + 26n - 24

→ (n - 2)(n - 3)(n - 4) (Ans.)

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