Question

1. which of the following are factors of $x^3 - 4x^2 - x + 4$?

select three correct answers.
a. $x + 1$
b. $x - 1$
c. $x + 2$
d. $x - 2$
e. $x + 4$
f. $x - 4$

Explanation:

Step1: Group polynomial terms

$x^3 - 4x^2 - x + 4 = (x^3 - 4x^2) + (-x + 4)$

Step2: Factor each group

$= x^2(x - 4) - 1(x - 4)$

Step3: Factor out common binomial

$= (x^2 - 1)(x - 4)$

Step4: Factor difference of squares

$= (x - 1)(x + 1)(x - 4)$

Answer:

A. $x + 1$, B. $x - 1$, F. $x - 4$