Question

What is the complete factorization of the polynomial below? x3 - 4x2 + x - 4

Answer 1

The complete factorization of the polynomial x³ - 4x² + x - 4 is (x - 2)(x + 2)(x - 1).

Step-by-step explanation:

The complete factorization of the polynomial x³ - 4x² + x - 4 is (x - 2)(x + 1)(x - 2).

To factorize the polynomial, we can start by looking for common factors. In this case, we can factor out (x - 2) since it appears twice in the polynomial.

After factoring out (x - 2), we are left with (x - 2)(x² + x - 2). To further factorize the quadratic expression x² + x - 2, we can use the quadratic formula or look for two numbers that multiply to -2 and add up to 1. The factorization of x² + x - 2 is (x + 2)(x - 1).

Therefore, the complete factorization of the polynomial is (x - 2)(x + 2)(x - 1).

Answer 2

`\huge\boxed{x^3-4x^2+x-4=(x-4)(x^2+1)}`

Step-by-step explanation:

`x^3-4x^2+x-4\qquad\text{distributive}\\\\=x^2(x-4)+1(x-4)\\\\=(x-4)(x^2+1)\\\\/x^2+1-\text{is prime}/`