Simplify the expression $\frac{12x^3+13x^2-59x+30}{4x-5}$

Step-by-step Solution

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Final answer to the problem

$3x^{2}+7x-6$
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Step-by-step Solution

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1

Divide $12x^3+13x^2-59x+30$ by $4x-5$

$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}-5;}{\phantom{;}3x^{2}+7x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}-5\overline{\smash{)}\phantom{;}12x^{3}+13x^{2}-59x\phantom{;}+30\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}-5;}\underline{-12x^{3}+15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-12x^{3}+15x^{2};}\phantom{;}28x^{2}-59x\phantom{;}+30\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-5-;x^n;}\underline{-28x^{2}+35x\phantom{;}\phantom{-;x^n}}\\\phantom{;-28x^{2}+35x\phantom{;}-;x^n;}-24x\phantom{;}+30\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-5-;x^n-;x^n;}\underline{\phantom{;}24x\phantom{;}-30\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}24x\phantom{;}-30\phantom{;}\phantom{;}-;x^n-;x^n;}\\\end{array}$
2

Resulting polynomial

$3x^{2}+7x-6$

Final answer to the problem

$3x^{2}+7x-6$

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Function Plot

Plotting: $3x^{2}+7x-6$

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0
a
b
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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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