What is the remainder when (x²⁷ + 51) is divided by (x + 1)?
The remainder theorem states that if you divide a polynomial f(x) by (x - h), then the remainder is f(h). Here f(x) = x²⁷ + 51 and it is being divided by {x - (-1)} ∴ Remainder = f(-1) f(-1) = (-1)²⁷ + 51 ⇒ f(-1) = -1 + 51 ⇒ f(-1) = 50 ⇒ Remainder = 50
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