Question

find the answer of question​

Answer 1

Let p(x) = 4x³ - 12x² + 14x - 3

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 g(x) then the remainder is p{ zero of the g(x)}.

=> Let g(x) = 2x - 1

To Zero of g(x) equate g(x)=0

2x - 1 = 0

2x = 1

x = 1/2

So by remainder theorem p(1/2) is the remainder of p(x)

To know the remainder of p(x) substitute x = 1/2 in p(x)

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 +  4

= {1 - 3(2) + 4(2)}/2

= (1 - 6 + 8)/2

= 3/2