Question

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

Answer 1

Answer:

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Step-by-step explanation:

According to remainder theorem, We know if f(x) is divided by ( x - a) , then remainder = f(a) ,

If f(x) is divided by (x-a) we have taken it (x -a) = 0 .So, Remainder would be f(a) .

Now, p(x) = 4x³ -12x²+14x - 3 .

If p(x) is divided by 2x-1 , then (2x-1) = 0 , x = 1/2 .So when p(x) is divided by (2x-1) , it leaves a remainder p(1/2)

p(1/2)

= 4(1/2)³ -12(1/2)²+14(1/2)-3

= 4(⅛)-12(1/4)+7-3

= 1/2 -3 + 7 - 3

= 1/2 +1

= 3/2

The remainder when 4x³-12x²+14x-3 divided by 2x-1 is 3/2

Answer 2

Answer:

$\huge{\boxed{\rm{\orange{Remainder=3/2}}}}$

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