Question

using remainder theorem; find the remainder when P( x ) is divided by G (x),where
P(x) =x^3 - 3 x^2+4x+50 and
G(x) =x-3​

Answer 1

Answer:

Solution :

(i) given p(x)=x 3−2x 2−4x−1and g(x)=x+1

Here , zero of g(x) is -1

when we divide p(x) g(x) using remaining theorem , we get the remainder p-13).

∴p−(−1)=(−1)3−2(−1)2−4(−1)−1

=−1−2+4−1

=4−4=0

Hence , remainder is 0.

(ii) Given −p(x)=x 3−3x+4x+50 and g(x)=x−3

Here ,zero pf g(x) is 3.

when we divide p(x)by g(x) using remainder theorem , we get the remainder p(3).

∴p(3)=(3)3−3(3)2+4(3)+50

=27−27+12+50=62

Hence , remainder is 62.

(iii) Given p(x)=4x 3−12x 2+14x−3and=2x−1

here , zero of g(x) is 12

when we divide p(x) by g(x) using reminder theorem, we get the remainder p(12)

∴p(12)=4(12)3−12(12)2+14(12)−3=4×18−12×14+14×12−3

=12−3+7−3=12+1=1+22=32

Hence , remainder is 32 .

(iv) Given ,p(x)= x 3−6 x 2+2x−4and g(x)=1−32x.

Here , zero of g(x) is 23.

when we divide p(x) by g(x) using remainder theorem , we get the reminder p(23) .

∴=827−6×49=2×23−4=827−249+43−4

=8−72+36−108/27=−136/27

hence remainder is −136/27

Step-by-step explanation:

Answer 2

Answer:

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