Q. 55.0( 4 Votes )

# In each of the following, using the remainder theorem, find the remainder when *f*(*x*) is divided by *g*(*x*):

*f*(*x*) = *x*^{3}-6*x*^{2}+2*x*-4, *g*(*x*) = 1-2*x*

Answer :

We have,

*f*(*x*) = *x*^{3}-6*x*^{2}+2*x*-4 and *g*(*x*) = 1-2*x*

Therefore, by remainder theorem when f (x) is divided by g (x) = -2 (x - ), the remainder is equal to f ()

Now, *f*(*x*) = *x*^{3}-6*x*^{2}+2*x*-4

f () = ()^{3} – 6 ()^{2} + 2 () – 4

= - + 1 – 4

=

Hence, required remainder is

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is divided by (x-a)

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