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Show that (X – 1) is a Factor of X3 – 7x2 + 14x – 8. Hence, Completely Factorise the Given Expression. - ICSE Class 10 - Mathematics

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Question

Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.

Solution

let `f(x)=x^3-7x^2+14x-8` 

`f(1)=(1)^3-7(1)^2+14(1)-8=1-7+14-8=0` 

Hence, (x-1) is a factor of f(x) 

 

∴` x^3-7x^2+14x-8=(x-1) (x^2-6x+8) `

                            =` (x-1)(x^2-2x-4x+8) `

                           =` (x-1)[x(x-2)-4(x-2)] `

                           =`(x-1) (x-2) (x-4)`

  Is there an error in this question or solution?
Solution Show that (X – 1) is a Factor of X3 – 7x2 + 14x – 8. Hence, Completely Factorise the Given Expression. Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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