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# Divide $x^4-2x^3-11x^2+30x-20$ by $x^2+3x-2$

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##  Final answer to the problem

$x^{2}-5x+6+\frac{2x-8}{x^2+3x-2}$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Write in simplest form
• 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
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1

Divide $x^4-2x^3-11x^2+30x-20$ by $x^2+3x-2$

$\begin{array}{l}\phantom{\phantom{;}x^{2}+3x\phantom{;}-2;}{\phantom{;}x^{2}-5x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}-2x^{3}-11x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-2;}\underline{-x^{4}-3x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3}+2x^{2};}-5x^{3}-9x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-2-;x^n;}\underline{\phantom{;}5x^{3}+15x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}+15x^{2}-10x\phantom{;}-;x^n;}\phantom{;}6x^{2}+20x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-2-;x^n-;x^n;}\underline{-6x^{2}-18x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;;-6x^{2}-18x\phantom{;}+12\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}2x\phantom{;}-8\phantom{;}\phantom{;}\\\end{array}$
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Resulting polynomial

$x^{2}-5x+6+\frac{2x-8}{x^2+3x-2}$

##  Final answer to the problem

$x^{2}-5x+6+\frac{2x-8}{x^2+3x-2}$

##  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

SnapXam A2

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7
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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

###  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.