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Simplify the expression $\frac{x^4+x+1}{x-0.685}$

Step-by-step Solution

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Final Answer

$x^{3}+0.685x^{2}+\frac{61}{130}x+\frac{37}{28}+\frac{1.905172}{x-0.685}$
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Step-by-step Solution

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1

Divide $x^4+x+1$ by $x-0.685$

$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-0.685;}{\phantom{;}x^{3}+0.685x^{2}+\frac{61}{130}x\phantom{;}+\frac{37}{28}\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-0.685\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}+x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-0.685;}\underline{-x^{4}+0.685x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+0.685x^{3};}\phantom{;}0.685x^{3}\phantom{-;x^n}+x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-0.685-;x^n;}\underline{-0.685x^{3}+\frac{61}{130}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-0.685x^{3}+\frac{61}{130}x^{2}-;x^n;}\phantom{;}\frac{61}{130}x^{2}+x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-0.685-;x^n-;x^n;}\underline{-\frac{61}{130}x^{2}+\frac{9}{28}x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-\frac{61}{130}x^{2}+\frac{9}{28}x\phantom{;}-;x^n-;x^n;}\phantom{;}\frac{37}{28}x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-0.685-;x^n-;x^n-;x^n;}\underline{-\frac{37}{28}x\phantom{;}+0.905172\phantom{;}\phantom{;}}\\\phantom{;;;-\frac{37}{28}x\phantom{;}+0.905172\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}1.905172\phantom{;}\phantom{;}\\\end{array}$
2

Resulting polynomial

$x^{3}+0.685x^{2}+\frac{61}{130}x+\frac{37}{28}+\frac{1.905172}{x-0.685}$

Final Answer

$x^{3}+0.685x^{2}+\frac{61}{130}x+\frac{37}{28}+\frac{1.905172}{x-0.685}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (x^4+x)/(x-0.685) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $x^{3}+0.685x^{2}+\frac{61}{130}x+\frac{37}{28}+\frac{1.905172}{x-0.685}$

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5
6
7
8
9
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

How to improve your answer:

Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

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