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Simplify the expression $\frac{x^7-128}{x-2}$

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Final answer to the problem

$x^{6}+2x^{5}+4x^{4}+8x^{3}+16x^{2}+32x+64$
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We can factor the polynomial $x^7-128$ using the rational root theorem, which guarantees that for a polynomial of the form $a_nx^n+a_{n-1}x^{n-1}+\dots+a_0$ there is a rational root of the form $\pm\frac{p}{q}$, where $p$ belongs to the divisors of the constant term $a_0$, and $q$ belongs to the divisors of the leading coefficient $a_n$. List all divisors $p$ of the constant term $a_0$, which equals $-128$

$1, 2, 4, 8, 16, 32, 64, 128$

Learn how to solve polynomial long division problems step by step online.

$1, 2, 4, 8, 16, 32, 64, 128$

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Learn how to solve polynomial long division problems step by step online. Simplify the expression (x^7-128)/(x-2). We can factor the polynomial x^7-128 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -128. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^7-128 will then be. Trying all possible roots, we found that 2 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.

Final answer to the problem

$x^{6}+2x^{5}+4x^{4}+8x^{3}+16x^{2}+32x+64$

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Plotting: $x^{6}+2x^{5}+4x^{4}+8x^{3}+16x^{2}+32x+64$

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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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