the polynomial ax^3+3x^2-13 and 2x^3-5x+a are divided by x+2 . if the remainder in each case is the same , find the value of a.

Answers (1)

solution : Let p(x)=ax^3+3x^2-13 and q(x)=2x^3-5x+a  be the given polynomials.

                 the remainder whenp(x)  and  q(x)  are divided by (x+2)  are p(-2)   and q(-2)  respectively .

               By the given condition , we have 

                              p(-2)=q(-2)

Rightarrow                         a(-2)^3+3(-2)^2-13 =2(-2)^3-5(-2)+a

Rightarrow                           -8a+12-13=-16+10+a  Rightarrow-9a =-5  Rightarrowa=  frac59

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