Factor Theorem-3

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If the polynomial f (x) = 2x³ -ax² + 4x - 1 leaves a remainder - 37 when divided by x + 2, find the value of a.

Solution: By remainder theorem, when f(x) is divided by x + 2, the remainder = f (-2)

f (-2) = 2 (-2)³ - a(-2)² + 4(-2) - 1

= - 16 - 4a - 8 - 1

= - 25 - 4a

Given Remainder = - 37

=> - 25 - 4a = - 37

=> 4a = 37 - 25 = 12

=> a = 12 / 4 = 3