Solving Polynomials - Answers to Common Questions

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Homework Help Overview

The discussion revolves around solving polynomial equations, specifically focusing on determining coefficients in polynomial expressions. The original poster presents two polynomial equations and seeks assistance in finding unknown coefficients.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss substituting specific values of x to simplify the equations and eliminate certain polynomial terms. There is an emphasis on using the roots of the polynomial to derive equations involving the unknown coefficients.

Discussion Status

Some participants have offered guidance on how to approach the problem by suggesting specific values for substitution. Multiple interpretations of the problem setup are being explored, particularly regarding the role of the polynomial Q(x) and P(x) in the equations.

Contextual Notes

There is an indication that the original poster is new to the topic of polynomials, which may affect their understanding of the problem-solving process. The discussion includes assumptions about the degree of the polynomials involved.

Kyoma
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i'm pretty new to polynomials and I have qns, which I do not know how to solve.

x5 + ax3 + bx2 - 3 = (x2 - 1)Q(x)- x - 2

Q(x) is a polynomial. Solve a and b.

I know the degree of Q(x) is 3, so I subst Q(x) into x3, but I got stuck.

Help. Thanks in advance.
 
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You don't need to know what Q(x) is. The zeroes of [tex]x^2-1[/tex] are [tex]x=\pm 1[/tex] so if you substitute x=1 into the entire equality, that Q(x) part cancels since anything times zero is zero (your 'anything' is the Q(x)) and then you'll get an equation in a and b. Then substitute the other value of x to get another equation in a and b. Solve simultaneously and you're done! :smile:
 
Thank you very much.

How about this:

4x3 + 5x - 2 = (x+2)(x-1)P(x) + ax + b

Find a and b. Last qns, I seriously can't solve!
 
If you thought a bit more about what I posted you should have picked up on what to do. What values of x can you choose so that you eliminate the P(x)?
 

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