Question

Using reminder theorem find remainder when f(x) =4x^3-12x^2+11x-3 is divided by g(x) =x+1/2

Answer 1

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Answer 2

Remainder is (-12).

Explanation:

g(x) = x+1/2

x = -1/2

By the remainder theorem, we know that when f(x) is by (x+1/2), the remainder is f(-1/2)

Now,

f(-1/2) = [4 * (-1/2)³ - 12 * (-1/2) ² + 11 (-1/2) - 3 ] -> (i)

WKT,

(-1/2)³ = (-1/2) * (-1/2) * (-1/2)

= 0.125 = 1/8 -> (a)

(-1/2) ² = (-1/2) * (-1/2)

= 0.25 = 1/4 -> (b)

substitute equation (a) and (b) in (i)

=  [4 * (-1/2)³ - 12 * (-1/2) ² + 11 (-1/2) - 3]

= [ 4 * (-1/8)  - 12 * (1/4) + 11 (-1/2) - 3]

= [ (-1/2) - 3 - 11/2 - 3]

= [-1/2 -3 - 11/2 -3]

= -1/2 - 11/2 - 3 - 3

= -1/2 - 11/2 -6

taking LCM,

= -1 + (-11) + (-2) 6 / 2

= -1-11-2(6)/2

= -24/2

= -12

Therefore, Remainder is (-12).

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