Question

Find the remainder when p(x)= 4x³ - 12x² + 14x − 3 is divided by g(x) = x -1/2​

Answer 1

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).

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.