# 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.

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

the remainder when$p(x)$  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$  $\Rightarrow$a=  $\frac{5}{9}$

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