If 2*x^2*+ *x *+ *m *is divisible by *x *- 2, then it is also divisible by

A. *x *+ 3

B. 2*x *– 3

C. 2*x *+3

D. 2*x *– 5

E. 2*x *+ 5

### 1 Answer | Add Yours

`f(x) = 2x^2 +x + m`

Since f(x) is divisible by (x-2) then by remainder theorem;

`f(2)=0`

`f(2) = 2(2)^2 + 2+m =0`

`m= -10`

`f(x) = 2x^2+x-10`

`2x^2+x-10`

`= 2x^2+5x-4x-10`

`=2x^2 -4x +5x – 10`

`= 2x (x-2)+5(x-2)`

`=(x-2)(2x+5)`

*So the other factor is (2x+5). f(x) is divisible by (2x+5). Correct answer is E).*

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