Question

x^3+3x^2+3x+1 divided by 5+2x​

Answer 1

$\mathfrak{Apply \: remainder \: theroem}$

$5+2x=$

$2x=-5$

$\boxed{x={\frac{5}{2}}}$

$replace \: x \: by \:-5/2 , we \: get \:</p><p>x3+3x2+3x+1$

= $({\frac{-5}{2})3+3({\frac{-5}{2})2+3({\frac{-5}{2})+1}}}$

= $\frac{-125}{8}+{\frac{75}{4}-{\frac{15}{2}+1}}$

= $(-125+150-60+8)/125$

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

$\boxed{\boxed{therefore \: the \: remainder \: is \: {\frac{-27}{8} }}}$

Answer 2

Answer:

$\huge\underline\bold\red{Answer!!}$

$remainder = - \dfrac {27}{8}$

Step-by-step explanation:

Given information:-

$dividend = x {}^{3} + 3x {}^{2} + 3x + 1$

$divisor = 5 + 2x$

We need to find the remainder of

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

Using long division method we get

$\dfrac{x {}^{3} + 3x {}^{2} + 3x + 1}{5 + 2x} =$

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

$the \:remainder \: is \: -\dfrac{27}{8}$