Sketch of x^3-2x^2+5 using synthetic division

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Homework Help Overview

The discussion revolves around sketching the function f(x) = x^3 - 2x^2 + 5, with a focus on using synthetic division to analyze the polynomial.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss finding factors of the polynomial and using synthetic division to simplify it. There are attempts to identify roots and turning points, as well as questions about the setup of synthetic division.

Discussion Status

Some participants have provided guidance on finding factors and suggested checking specific values. There is an acknowledgment of the complexity of the problem, and some participants are exploring whether a simpler approach might suffice for sketching the function.

Contextual Notes

Participants note uncertainty regarding the necessity of finding intercepts and the appropriateness of the problem's complexity given its homework context.

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Homework Statement


sketch f(x)=x^3-2x^2+5


Homework Equations


none


The Attempt at a Solution


i tried to uses synthetic division to bring it down to a lower power, but i can't remember what to do because i don't know any of the factors...
 
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Well first you would try to find factors such that f(a)=0, if f(a)=0 then (x-a) is a factor of f(x).

Seeing as how the last number there is 5, then you should try,1,-1,-5,5 and see if any are zero.

If you do not find it to be zero,then either it has complex roots or non-integer roots.
find where it cuts the f(x)-axis and x-axis. Find turning points(and whether they are max or min points) and try to sketch. If you need more help, reply back
 
it didnt work... and seeing as this was a homework question i don't think my teacher would have made it so complex...did i set up the synthetic division correctly?

5 | 1 -2 0 5
________
________
 
yea...i set it up right..turns out that i didnt need to find the intercepts, and couldve just aproximated a sketch
 

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