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Simplify the expression $\frac{3x^3+2x^2-5x}{2x^5-4x^3+6x^2-8x+10}$

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Solution

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Final answer to the problem

$\frac{3x^3+2x^2-5x}{2\left(x^{5}-2x^{3}+3x^2-4x+5\right)}$
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Step-by-step Solution

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  • Write in simplest form
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
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Factor the polynomial $2x^5-4x^3+6x^2-8x+10$ by it's greatest common factor (GCF): $2$

$\frac{3x^3+2x^2-5x}{2\left(x^{5}-2x^{3}+3x^2-4x+5\right)}$

Final answer to the problem

$\frac{3x^3+2x^2-5x}{2\left(x^{5}-2x^{3}+3x^2-4x+5\right)}$

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Function Plot

Plotting: $\frac{3x^3+2x^2-5x}{2\left(x^{5}-2x^{3}+3x^2-4x+5\right)}$

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1
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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
D□x
∫
∫◻
|◻|
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:

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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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