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Factor the expression $x^4+x^3-6x^2-4x+8$

Step-by-step Solution

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Final Answer

$\left(x+2\right)^2\left(x-1\right)\left(x-2\right)$
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Step-by-step Solution

Problem to solve:

$x^4+x^3-6x^2-4x+8$

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We can factor the polynomial $x^4+x^3-6x^2-4x+8$ 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 $8$

$1, 2, 4, 8$

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$1, 2, 4, 8$

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Learn how to solve problems step by step online. Factor the expression x^4+x^3-6x^2-4x+8. We can factor the polynomial x^4+x^3-6x^2-4x+8 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 8. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^4+x^3-6x^2-4x+8 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

$\left(x+2\right)^2\left(x-1\right)\left(x-2\right)$

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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

SimplifyFactorFactor by completing the squareFind the integralFind the derivativeFind x^4+x^3 using the definitionFind the rootsFind break even pointsFind the discriminant

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x
y
z
.
(◻)
+
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◻/◻
/
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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

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