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Question

What polynomial added to x2+4x5 gives 2x23x+1?

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Solution

Let the polynomial that should be added to the polynomial x2+4x5 be A, so that the resulting polynomial is 2x23x+1. Therefore, we have:

(x2+4x5)+A=2x23x+1A=(2x23x+1)(x2+4x5)A=2x23x+1x24x+5A=(2x2x2)+(3x4x)+(1+5)A=x27x+6

Hence, x27x+6 should be added to the polynomial x2+4x5, so that the resulting polynomial is 2x23x+1.

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