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# Factor the expression $x^3+9x^2+27x+27$

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##  Final answer to the problem

$\left(x+3\right)^{3}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
• Prove from LHS (left-hand side)
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1

We can factor the polynomial $x^3+9x^2+27x+27$ 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 $27$

$1, 3, 9, 27$

Learn how to solve polynomial factorization problems step by step online.

$1, 3, 9, 27$

Learn how to solve polynomial factorization problems step by step online. Factor the expression x^3+9x^227x+27. We can factor the polynomial x^3+9x^2+27x+27 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 27. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3+9x^2+27x+27 will then be. Trying all possible roots, we found that -3 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

$\left(x+3\right)^{3}$

##  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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4
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
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 Factorization

They are a group of techniques that help us rewrite polynomial expressions as a product of factors.

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