2017 · Q16
Let f(x)=a₀ xⁿ+a₁ xⁿ⁻¹ +a₂ xⁿ⁻²+… + aₙ₋₁ x + aₙ, where a₀, a₁, a₂, …, aₙ are real numbers. If f(x) is divided by (a x-b), then the remainder is
Elementary MathematicsAlgebra
- Af(b/a)
- Bf(-b/a)
- Cf(a/b)
- Df(-a/b)
Explanation
By the remainder (factor) theorem, dividing any polynomial f(x) by (ax−b) leaves remainder f(b/a), since ax−b = 0 exactly at x = b/a. Hence option (A) f(b/a). (Trap: −b/a is the zero of ax+b, not ax−b.)