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Factorise x3 + 6x2 + 11x + 6 completely using factor theorem. - ICSE Class 10 - Mathematics

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Question

Factorise x3 + 6x2 + 11x + 6 completely using factor theorem. 

Solution

`"Let"  f(x)=x^3+6x^2+11x+6 `

`for=x=-1 `

`f(-1)=(-1)^3+6(-1)^2+11(-1)+6` 

`=-1+6-11+6=12-12=0 `

Hence, (x+1) is a factory of f(x) 

 

∴ `x^3+6x^2+11x+6=(x+1)(x^2+5x+6) `

                              =`(x+1)(x^2+2x+3x+6) `

                             =`(x+1)[x(x+2)+3(x+2)] `

                              =`(x+1)(x+2)(x+3)`

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Solution Factorise x3 + 6x2 + 11x + 6 completely using factor theorem. Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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