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Simplify the expression $\frac{-144x^4+104x^3-73x^2+26x-3}{324x^4+360x^3+208x^2+60x+9}$

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Final Answer

$-\frac{4}{9}+\frac{264x^{3}+\frac{175}{9}x^{2}+\frac{158}{3}x+1}{324x^4+360x^3+208x^2+60x+9}$
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Step-by-step Solution

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1

Divide $-144x^4+104x^3-73x^2+26x-3$ by $324x^4+360x^3+208x^2+60x+9$

$\begin{array}{l}\phantom{\phantom{;}324x^{4}+360x^{3}+208x^{2}+60x\phantom{;}+9;}{-\frac{4}{9}\phantom{;}\phantom{;}}\\\phantom{;}324x^{4}+360x^{3}+208x^{2}+60x\phantom{;}+9\overline{\smash{)}-144x^{4}+104x^{3}-73x^{2}+26x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}324x^{4}+360x^{3}+208x^{2}+60x\phantom{;}+9;}\underline{\phantom{;}144x^{4}+160x^{3}+\frac{832}{9}x^{2}+\frac{80}{3}x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}144x^{4}+160x^{3}+\frac{832}{9}x^{2}+\frac{80}{3}x\phantom{;}+4\phantom{;}\phantom{;};}\phantom{;}264x^{3}+\frac{175}{9}x^{2}+\frac{158}{3}x\phantom{;}+1\phantom{;}\phantom{;}\\\end{array}$
2

Resulting polynomial

$-\frac{4}{9}+\frac{264x^{3}+\frac{175}{9}x^{2}+\frac{158}{3}x+1}{324x^4+360x^3+208x^2+60x+9}$

Final Answer

$-\frac{4}{9}+\frac{264x^{3}+\frac{175}{9}x^{2}+\frac{158}{3}x+1}{324x^4+360x^3+208x^2+60x+9}$

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 (-144x^4+104x^3)/(324x^4+360x^3) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $-\frac{4}{9}+\frac{264x^{3}+\frac{175}{9}x^{2}+\frac{158}{3}x+1}{324x^4+360x^3+208x^2+60x+9}$

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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

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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