Question

find remainder when a polynomial p(x)=x^3+3x^2+3x+1 is divided by x-1/2​

Answer 1

Answer:

The remainder is $\sf{\dfrac{27}{8}}$

Step-by-step explanation:

Solution :

Remainder theorem is used to solve the given Question.

p(x) = x³ + 3x² + 3x + 1

Divided by = x - $\sf{\frac{1}{2}}$

Equate divisor to 0,

⇒ x - $\sf{\frac{1}{2}}$ = 0

⇒ x = $\sf{\frac{1}{2}}$

In p(x) = x³ + 3x² + 3x + 1 (Putting the value of x)

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

= 1/8 + 3/4 + 3/2 + 1

= (1 + 6 + 12 + 8)/8

= 27/8

The remainder = $\sf{\dfrac{27}{8}}$

Therefore, the remainder is $\sf{\dfrac{27}{8}}$