Exercise
$x^4+8x^3+14x^2-8x-15$
Step-by-step Solution
Learn how to solve special products problems step by step online. Factor the expression x^4+8x^314x^2-8x+-15. We can factor the polynomial x^4+8x^3+14x^2-8x-15 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 -15. 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+8x^3+14x^2-8x-15 will then be. Trying all possible roots, we found that -5 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.
Factor the expression x^4+8x^314x^2-8x+-15
Final answer to the exercise
$\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x-1\right)$