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

Step-by-step Solution

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$\left(x+1\right)\left(x-3\right)\left(x-1\right)$
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 Step-by-step Solution 

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

$1, 3$

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

$1, 3$

Learn how to solve polynomial factorization problems step by step online. Factor the expression x^3-3x^2-x+3. We can factor the polynomial x^3-3x^2-x+3 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 3. 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-x+3 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.

$\left(x+1\right)\left(x-3\right)\left(x-1\right)$

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SimplifyFactorFactor by completing the squareFind the integralFind the derivativeFind x^3+-3x^2 using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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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

Main Topic: Polynomial Factorization

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