contestada

Divide the polynomials.
The form of your answer should either be p(x)p(x)p, left parenthesis, x, right parenthesis or p(x)+\dfrac{k}{x+1}p(x)+
x+1
k
​
p, left parenthesis, x, right parenthesis, plus, start fraction, k, divided by, x, plus, 1, end fraction where p(x)p(x)p, left parenthesis, x, right parenthesis is a polynomial and kkk is an integer.
\dfrac{3x^3+x-11}{x+1}=
x+1
3x
3
+x−11
​
=start fraction, 3, x, cubed, plus, x, minus, 11, divided by, x, plus, 1, end fraction, equals

Respuesta :

Answer:

[tex]\dfrac{3x^3+x-11}{x+1}=3x^2-3x+4-\dfrac{15}{x+1}[/tex]

Step-by-step explanation:

We want to determine the result of the quotient: [tex]\dfrac{3x^3+x-11}{x+1}[/tex]

We follow the procedure of long division which is set out int he table below.

[tex]\left|\begin{array}{c|c}&3x^2-3x+4\\-----&-----\\x+1&3x^3+x-11\\Subtract&-(3x^3+3x^2)\\&------\\&-3x^2+x-11\\Subtract&-3x^2-3x\\&------\\&4x-11\\Subtract&4x+4\\&------\\&-15\end{array}\right|[/tex]

Therefore:

[tex]\dfrac{3x^3+x-11}{x+1}=3x^2-3x+4-\dfrac{15}{x+1}[/tex]