Find the first degree polynomial p(x) with p(0)=1 and p(1)=2

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Find the first degree polynomial p(x) with p(0)=1 and p(1)=2

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Answer:let the polynomial be p(x)

p(x) = ax + b (where a and b are constants)

p(1) = a + b = 1 – (1) (given in the question)

p(2) = 2a + b = 3 – (2) (given in the question)

by (1) and (2)

a = 2, b = -1

⇒ p(x) = 2x – 1