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Factor the expression $27x^3+135x^2+225x+125$

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Final answer to the problem

$\left(3x+5\right)^{3}$
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We can factor the polynomial $27x^3+135x^2+225x+125$ 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 $125$

$1, 5, 25, 125$

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$1, 5, 25, 125$

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Learn how to solve factorization problems step by step online. Factor the expression 27x^3+135x^2225x+125. We can factor the polynomial 27x^3+135x^2+225x+125 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 125. Next, list all divisors of the leading coefficient a_n, which equals 27. The possible roots \pm\frac{p}{q} of the polynomial 27x^3+135x^2+225x+125 will then be. Trying all possible roots, we found that -\frac{5}{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

$\left(3x+5\right)^{3}$

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Plotting: $\left(3x+5\right)^{3}$

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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

How to improve your answer:

Main Topic: Factorization

In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

Used Formulas

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