Question

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = x³ -6x²+2x-4, g(x) = 1-2x

Answer 1

Given : f(x) = x³ - 6x² + 2x - 4, g(x) = 1 - 2x

 

By remainder theorem,  when f(x) is divided by g(x) = 1 - 2x , the remainder is equal to f(½ ) :  

Now, f(x) =  x³ - 6x² + 2x - 4

f (½ ) =  (½)³ - 6(½)² + 2( ½) - 4

f (½ ) = (1/8) - 6(¼ ) + 2/2 - 4

f (½ ) = ⅛ - 3/2 + 1 - 4

f (½ ) = ⅛ - 3/2 - 3

f (½ ) = (1 - 12 - 24)/8

f (½ ) = (-11 - 24)/8

f (½ ) = - 35/8

Hence, the remainder when f(x) is divided by g(x) is - 35/8.

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Answer 2

$\bf \green{solution}$

• g(x) = 1-2x=0

=>x=1/2

Now,

f(x) =  x³ - 6x² + 2x - 4

putting the value of x

f (½ ) =  (½)³ - 6(½)² + 2( ½) - 4

f (½ ) = (1/8) - 6(¼ ) + 2/2 - 4

f (½ ) = 1/8- 3/2 + 1 - 4

f (½ ) = 1/8 - 3/2 - 3

f (½ ) = (1 - 12 - 24)/8

f (½ ) = (-11 - 24)/8

f (½ ) = - 35/8

Learn more:

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):f(x) = x³+4x²-3x+10, g(x) = x+4

https://brainly.in/question/15903852