Question

x^3+6x^2+11x+6 factories​

Answer 1

Step-by-step explanation:

Question:- Factorise : x^3+6x^2+11x+6

Solution:-

f(x) = x^3+6x^2+11x+6

f(-1) = 1 + 6 - 11 + 6

= 12 - 12

= 0

∴ (x + 1) is a factor of f(x)

x^2 + 5x + 6

x + 1 ) x^3+6x^2+11x+6

x^3 + x^2

– –

━━━━━━━━━━━

5x^2+ 11x + 6

5x^2 + 5x

– –

━━━━━━━━━━━━━

6x + 6

6x + 6

━━━━━━━━━━━━

0 0

=>Other factor = x^2 + 5x + 6

= x^2 + 3x +2x + 6 ( By splitting the middle term)

= x(x + 3)+2(x+3)

= (x +2)(x+3)

=> x^3+6x^2+11x+6 = (x+1)(x +2)(x+3) Ans.

:)