Confirm that (x-2) is a Factor of x^3 - 2x^2 + x - 2

  • Thread starter Thread starter nae99
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around confirming whether (x-2) is a factor of the polynomial x^3 - 2x^2 + x - 2. Participants are exploring the implications of the polynomial's evaluation at a specific point.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants attempt to evaluate the polynomial at x = 2 and discuss the significance of the result. Questions are raised about the simplification of the expression and the implications of finding f(2) = 0.

Discussion Status

The discussion is progressing with participants confirming that f(2) = 0 suggests that (x-2) is a factor of the polynomial. Some participants are also prompted to consider polynomial long division as a method to further explore the factorization.

Contextual Notes

There is a note that the polynomial is not an equation due to the absence of an equal sign, which may influence the understanding of the problem context.

nae99
Messages
129
Reaction score
0

Homework Statement



show that (x-2) is a factor of x^3 - 2x^2 + x - 2

Homework Equations





The Attempt at a Solution



f(2) = 2^3 - 2(2)^2 + 2 - 2

is that any good
 
Physics news on Phys.org
nae99 said:

Homework Statement



show that (x-2) is a factor of x^3 - 2x^2 + x - 2

Homework Equations





The Attempt at a Solution



f(2) = 2^3 - 2(2)^2 + 2 - 2

is that any good
What does 2^3 - 2(2)^2 + 2 - 2 simplify to?
 
mark44 said:
what does 2^3 - 2(2)^2 + 2 - 2 simplify to?

= 8 - 8 + 2 - 2
= 0
 
OK, that's better. Now, you have f(2) = 0, where apparently f(x) = x^3 - 2x^2 + x - 2. If f(a) = 0, what does that tell you about x - a being a factor of f(x)?
 
Mark44 said:
OK, that's better. Now, you have f(2) = 0, where apparently f(x) = x^3 - 2x^2 + x - 2. If f(a) = 0, what does that tell you about x - a being a factor of f(x)?

that it is a factor of the equation
 
nae99 said:
that it is a factor of the equation
That x - 2 is a factor of x^3 - 2x^2 + x - 2.

Note that x^3 - 2x^2 + x - 2 is not an equation (there's no equal sign).
 
Mark44 said:
That x - 2 is a factor of x^3 - 2x^2 + x - 2.

Note that x^3 - 2x^2 + x - 2 is not an equation (there's no equal sign).

oh ok, got it
 
nae99 said:
show that (x-2) is a factor of x^3 - 2x^2 + x - 2

There is nothing stopping you dividing x^3 - 2x^2 + x - 2
by x-2
and showing that there is 0 remainder.

Can you do that? Try it like you'd do long division, where the first "digit" of the answer will be x^2.


x-2 ) x^3 - 2x^2 + x - 2 [/color]
 

Similar threads

Solve ##x^{\frac{-1}{2}}-2x^{\frac{1}{2}}+x^{\frac{2}{3}}=0##
  • · Replies 24 ·
Replies
24
Views
4K
Show that if ##x>1##, ##\log_e\sqrt{x^2-1}=\log_ex-\dfrac{1}{2x^2}-##
  • · Replies 8 ·
Replies
8
Views
2K
Solve ##\dfrac{3x-6}{5-x}+\dfrac{11-2x}{10-4x}=3\dfrac{1}{2}##
  • · Replies 3 ·
Replies
3
Views
3K
Solve the problem involving the cubic function
  • · Replies 12 ·
Replies
12
Views
2K
Solve ##\left| x+3 \right|= \left| 2x+1\right|##
  • · Replies 7 ·
Replies
7
Views
4K
Solve the simultaneous equations involving x, y, and their squares
  • · Replies 2 ·
Replies
2
Views
2K
Rationalize the denominator: ##\sqrt{\dfrac{1}{2x^3y^5}}##
  • · Replies 6 ·
Replies
6
Views
3K
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
  • · Replies 10 ·
Replies
10
Views
2K
Factoring difference of squares not working?
  • · Replies 3 ·
Replies
3
Views
3K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
  • · Replies 8 ·
Replies
8
Views
5K