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Question Number 129090 by Adel last updated on 12/Jan/21

$$\mathrm{p}\left(\mathrm{x}\right)+\mathrm{p}(\mathrm{x}+2)={2\mathrm{X}}^2+2\mathrm{X}+4\mathbf{p}\left(\mathbf{x}\right)=?$$

Answered by MJS_new last updated on 12/Jan/21

$$p\left(x\right)={ax}^2+bx+c$$$$p(x+2)={ax}^2+(4a+b)x+(4a+2b+c)$$$$\Rightarrow$$$$2{ax}^2+2(2a+b)x+2(2a+b+c)=2x^2+2x+4$$$$\Rightarrow a=1\wedge b=-3\wedge c=-1$$$$\Rightarrow$$$$p\left(x\right)=x^2-3x-1$$

Commented by Adel last updated on 12/Jan/21

$$\mathrm{tanks}$$

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