Question

Find the remainder ,when f (x)=4x^3-12x^2+14x-3 is divided by x-1/2

Answer 1

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Let f(x) = 4x³ - 12x² + 14x - 3

& g(x) = ( x - ½ )

Then, g(x) = 0 ⇒ x - ½ ⇒ x = 0 + ½ ⇒ x = ½ = α

By Remainder Theorem; when f(x) is divided by g(x) then the remainder is f(α).

Now, f(α) = [ 4 × (½) ³ - 12 × (½)² + 14 × ½ - 3 ]

= 4 × ⅛ - 12 × ¼ + 14/2 - 3

= ½ - 3 + 7 - 3

= 3/2

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