Question

Consider the following polynomial function. f(x)=x⁴−3x³−9x² +15x - 20 factor the polynomial completely.

f(x) = ___

Answer 1

To factor the given polynomial completely, we first find the rational root using the Rational Root Theorem. Then, we use division to find the remaining factors. The fully factored polynomial is (x + 1)(x - 4)(x^2 + x - 5).

Step-by-step explanation:

To factor the polynomial completely, we need to find its roots. To do this, we first look for any rational roots using the Rational Root Theorem. The factors of the constant term -20 are ±1, ±2, ±4, ±5, ±10, and ±20. By testing these values in the polynomial function, we find that x = -1 is a root.

Using synthetic division or long division, we divide the polynomial by x + 1 to find the remaining factor as x^3 - 4x^2 + 5x - 20. Factoring this further, we have (x + 1)(x - 4)(x^2 + x - 5).