Step-by-step Solution

Factor the expression $x^3-3x^2-4x+12$

Go!
Go!
1
2
3
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

Final Answer

$\left(x+2\right)\left(x-3\right)\left(x-2\right)$
Got a different answer? Try our new Answer Assistant!

Step-by-step Solution

Problem to solve:

$factor\left(x^3-3x^2-4x+12\right)$

Choose the solving method

1

We can factor the polynomial $x^3-3x^2-4x+12$ 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 $12$

$1, 2, 3, 4, 6, 12$

Learn how to solve factorization problems step by step online.

$1, 2, 3, 4, 6, 12$

Unlock this full step-by-step solution!

Learn how to solve factorization problems step by step online. Factor the expression x^3-3x^2-4x+12. We can factor the polynomial x^3-3x^2-4x+12 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 12. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3-3x^2-4x+12 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

$\left(x+2\right)\left(x-3\right)\left(x-2\right)$
SnapXam A2
Answer Assistant

beta
Got another answer? Verify it!

Go!
1
2
3
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

Tips on how to improve your answer:

$factor\left(x^3-3x^2-4x+12\right)$

Main topic:

Factorization

Time to solve it:

~ 0.05 s