SOLUTION: Use the factor theorem so show that x - a is a factor of: x^2(a-b)^3 + a^2(b-x) + b^2(x-a) . I would appreciate it if you could help me with the steps.

Question 635576: Use the factor theorem so show that x - a is a factor of:
x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .
I would appreciate it if you could help me with the steps.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use the factor theorem to show that x - a is a factor of:
x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .
-------
Factor Theorem:: x-a is a factor iff f(a) = 0.
----
f(x) = x^2(a-b)^3 + a^2(b-x) + b^2(x-a)
---
f(a) = a^2(a-b)^3 + a^2(b-a) + b^2(a-a)
---
= a^2(a-b)^3 - a^2(a-b) + 0
---
= a^2(a-b)[(a-b)^2-1]
-------------
That result does not satisfy the Factor Theorem requirement.
x-a is NOT a factor of f(x)
===============================
Cheers,
Stan H.
===========
RELATED QUESTIONS
Use factor theorem ad synthetic division to determine which if the following is/are a... (answered by ikleyn)

Please help Use the Factor Theorem to determine whether x - c is a factor of f. If it... (answered by ewatrrr)

Hi, Please help me solve this math problem... Directions are :factor each expression as... (answered by Theo)

I was doing fine on my homework in till I came to a couple of questions that I could not... (answered by solver91311)

can you please help me to factorize the following 1. a^2(b+c)+b^2(c+a)+c^2(a+b)+2abc (answered by khwang)

Hello, I'm not sure where this problem is supposed to go so I just put it here. Use... (answered by josgarithmetic)

please help use the remainder theorem and the factor theorem to determin whether (b+4)... (answered by Nate)

A) Factor each polynomial completely, given that the binomial following it is a factor of (answered by stanbon)

find the product of (x-2y)^2 a. x^2+4y^2 b. x^2-4xy+4y^2 c. x^2+2xy+4y^2 d.... (answered by ewatrrr)