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Official Specimen Paper 2 · Q12

Paper 2Algebra

A polynomial p(x)p(x) has the property that p(1)=2p(1)=2.

Which one of the following can be deduced from this?

Ap(x)=(x−1)q(x)+2p(x)=(x-1)q(x)+2 for some polynomial q(x)q(x).
Bp(x)=(x+1)q(x)+2p(x)=(x+1)q(x)+2 for some polynomial q(x)q(x).
Cp(x)=(x−1)q(x)−2p(x)=(x-1)q(x)-2 for some polynomial q(x)q(x).
Dp(x)=(x+1)q(x)−2p(x)=(x+1)q(x)-2 for some polynomial q(x)q(x).
Ep(x)=(x−2)q(x)+1p(x)=(x-2)q(x)+1 for some polynomial q(x)q(x).
Fp(x)=(x+2)q(x)+1p(x)=(x+2)q(x)+1 for some polynomial q(x)q(x).
Gp(x)=(x−2)q(x)−1p(x)=(x-2)q(x)-1 for some polynomial q(x)q(x).
Hp(x)=(x+2)q(x)−1p(x)=(x+2)q(x)-1 for some polynomial q(x)q(x).

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