Step-by-step Solution

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

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Step-by-step explanation

Problem to solve:

$factor\left(x^4+x^3-6x^2-4x+8\right)$

Learn how to solve factorization problems step by step online.

$1, 2, 4, 8$

Unlock this full step-by-step solution!

Learn how to solve factorization 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

$\left(x+2\right)^2\left(x-1\right)\left(x-2\right)$
$factor\left(x^4+x^3-6x^2-4x+8\right)$

Main topic:

Factorization

Time to solve it:

~ 0.04 s (SnapXam)