Answer:
(x - 1)(x + 1)(x - 3).
Step-by-step explanation:
By the factor theorem if x - 3 is a factor then f (3) = 0.
f(3) = 3^3 - 3x^2 - x + 3 = 27 - 27 - 3 + 3 = 0
So, one factor is x-3.
Dividing the function by x-3:
x - 3)x^3 - 3x^2 - x + 3(x^2 - 1 <--- Quotient
x^3 - 3x^2
0 - x + 3
x^2 - 1 = (x - 1)(x + 1)
So, the factors are (x - 1)(x + 1)(x-3)
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Answer:
(x - 1)(x + 1)(x - 3).
Step-by-step explanation:
By the factor theorem if x - 3 is a factor then f (3) = 0.
f(3) = 3^3 - 3x^2 - x + 3 = 27 - 27 - 3 + 3 = 0
So, one factor is x-3.
Dividing the function by x-3:
x - 3)x^3 - 3x^2 - x + 3(x^2 - 1 <--- Quotient
x^3 - 3x^2
0 - x + 3
0 - x + 3
x^2 - 1 = (x - 1)(x + 1)
So, the factors are (x - 1)(x + 1)(x-3)