Question

find the remainder when p(x)=4x^3-12x^2+14x-3 is divided by g(x)= 2x-1 using reminder theorem
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Answer 1

Answer:

given p(x)=4x³-12x²+14x-3 is divided by g(x)=2x-1

2x-1=0

2x=1

x=1/2

now putting the value of x in p(x) equation

so, p(1/4)=4(1/2)³-12(1/2)²+14(1/2)-3

=4(1/8)-12(1/4)+7-3

=1/2-3+4

=1/2+1

taking l.c.m.

1/2*1+1/1*2

=1+2/2

3/2

Answer 2

Answer:

Remainder of the given problem is 3/2

Step-by-step explanation:

Step-by-step explanation:

Given polynomial p(x)=4x³-12x²+14x-3

and g(x)=2x-1

we know that by Remainder theorem

If p(x) is divided by (x-a) then the remainder is p(a)

now given g(x)=2x-1=0

=>2x=1

=>x=1/2

P(x) is divided by 2x-1 then the remainder is p(1/2).

p(1/2)=>4(1/2)³-12(1/2)²+14(1/2)-3

=>p(1/2)=>4(1/8)-12(1/4)+(14/2)-3

=>p(1/2)=4/8-12/4+14/2-3

=>p(1/2)=1/2-3+7-3

=>p(1/2)=1/2+7-6

=>p(1/2)=1/2+1

=>p(1/2)=(1+2)/2

=>p(1/2)=3/2

The remainder =3/2