Question

Find the remainder when
x^3+ 3x^2+ 3x + 1 is divided by
5 + 2x​

Answer 1

Answer:

Hope it helps you

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}.

Answer 2

Apply remainder theroem

5+2x=0

2x=-5

x=-5/2

replace x by -5/2, we get

x^3+3x^2+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