Question

x^2+3x^2+3x+1 divided by x-1/2. What is the remainder

Answer 1

Answer:

Remainder = 27/8

Explanation:

Let p(x) = x³+3x²+3x+1,

If p(x) divided by (x-1/2) then

the remainder is p(1/2).

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

Therefore,

Remainder = 27/8

••••

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Suppose p(x) = x³ + 3x² + 3x + 1

$\bf\huge\tt{\rightarrow x - \dfrac{1}{2}}$

$\bf\huge\tt{\rightarrow x = \dfrac{1}{2}}$

Remainder$\bf\huge\tt{\rightarrow p \dfrac{1}{2}}$

$\bf\huge\tt{\rightarrow p\dfrac{1}{2} = (\dfrac{1}{2})^3 + 3(\dfrac{1}{2})^2 + 3\dfrac{1}{2} + 1}$

$\bf\huge\tt{\rightarrow\dfrac{1}{8}+\dfrac{3}{4}+\dfrac{3}{2} + 1}$

$\bf\huge\tt{\rightarrow\dfrac{1+6+12+8}{8}}$

$\bf\huge\tt{\rightarrow\dfrac{27}{8}}$

Hence,

Remainder $\bf\huge\tt{\rightarrow\dfrac{27}{8}}$