If 2x^2+ x + m is divisible by x - 2, then it is also divisible by A. x + 3 B. 2x – 3 C. 2x +3 D. 2x – 5 E. 2x + 5

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`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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