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Factor the expression $\frac{x^3+x+5}{x+1}$

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Final answer to the problem

$\left(x-\frac{1}{2}\right)^2+\frac{7}{4}+\frac{3}{x+1}$
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Step-by-step Solution

How should I solve this problem?

  • Factor
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
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Divide $x^3+x+5$ by $x+1$

$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}+x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}-x^{2}+x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{2}+x\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;-2x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3\phantom{;}\phantom{;}\\\end{array}$

Learn how to solve factor problems step by step online.

$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}+x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}-x^{2}+x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{2}+x\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;-2x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3\phantom{;}\phantom{;}\\\end{array}$

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Learn how to solve factor problems step by step online. Factor the expression (x^3+x+5)/(x+1). Divide x^3+x+5 by x+1. Resulting polynomial. Add and subtract \displaystyle\left(\frac{b}{2a}\right)^2. Factor the perfect square trinomial x^2+-1x+\frac{1}{4}.

Final answer to the problem

$\left(x-\frac{1}{2}\right)^2+\frac{7}{4}+\frac{3}{x+1}$

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Plotting: $\left(x-\frac{1}{2}\right)^2+\frac{7}{4}+\frac{3}{x+1}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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