Question

p(x) = 4x³-12x²+14x-3;g(x)=2x-1 By remainder theorem, fi nd the remainder when, p(x) is divided by g(x)

Answer 1

$\bf \LARGE \it Hey \: User!!!$

given :-

p(x) = 4x³ - 12x² + 14x - 3

g(x) = 2x - 1
>> 2x - 1 = 0
>> 2x = 1
>> x = 1/2

on putting values :-

p(1/2) = 4(1/2)³ - 12(1/2)² + 14(1/2) - 3
= 4(1/8) - 12(1/4) + 7 - 3
= 1/2 - 3 + 7 - 3
= 1/2 + 1
= 1/2 + 2/2
= 3/2

hence, the remainder is 3/2

$\bf \LARGE \it Cheers!!!$

Answer 2

Hi ,

****************************************
Remainder Theorem :

Let p(x) be any polynomial of degree

greater than or equal to one and let

' a ' be any real number .

If p(x) is divided by the linear polynomial

(x-a) , then the remainder is p(a).

********************************************

Here ,

p(x) = 4x³-12x²+14x-3,

If p(x) divided by g(x)=2x-1 then

the remainder is p(1/2).

So, replace x by 1/2

p(1/2) = 4(1/2)³-12(1/2)²+14(1/2)-3

=4/8 - 12/4 + 14/2 - 3

= 1/2 - 3 + 7 - 3

= 1/2 + 7 - 6

= 1/2 + 1

= 3/2

Therefore ,

Required remainder = p(1/2) = 3/2

I hope this helps you.

: )