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Using the Remainder Theorem, Factorise Each of the Following Completely. 4x3 + 7x2 – 36x – 63 - ICSE Class 10 - Mathematics

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Question


Using the Remainder Theorem, factorise each of the following completely.  

4x3 + 7x2 – 36x – 63

Solution

`f(x)=4x^3+7x^2-36x-63` 

`for x=3 ` 

`f(x)=f(3)=4(3)^3+7(3)^2-36(3)-63` 

`=108+63-108-63=0` 

Hence,(x+3) is a factor of f(x) 

 

∴ `4x^3+7x^2-36x-63=(x+3)(4x^2-5x-21)` 

                                 `= (x+3)(4x^2-12x+7x-21)` 

                                `=(x+3)[4x(x-3)+7(x-3)] `

                                `=(x+3)(4x+7)(x-3)`

  

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Solution Using the Remainder Theorem, Factorise Each of the Following Completely. 4x3 + 7x2 – 36x – 63 Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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