Question

find the remainder when x3+3x2+3x+1 is divided by 5+2x

Answer 1

apply remainder theroem
5+2x=0
2x=-5
x=5/2
replace x by -5/2 , we get
x3+3x2+3x+1
= (-5/2)3+3(-5/2)2+3(-5/2)+1
= -125/8+75/4-15/2+1
= (-125+150-60+8)/125
= -27/8
therefore the remainder is -27/8

Answer 2

Answer:

$Remainder=-\frac{27}{8}$

Step-by-step explanation:

Given information:

$Dividend=x^3+3x^2+3x+1$

$Divisor=5+2x$

We need to find the remainder of

$\frac{x^3+3x^2+3x+1}{5+2x}$

Using long division method we get

$\frac{x^3+3x^2+3x+1}{5+2x}=\frac{x^2}{2} + \frac{x}{4} + \frac{7}{8} + -\frac{27}{8(5+2x)}$

Therefore the remainder is $-\frac{27}{8}$.