(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A polynomial [tex]P(x)=(x-b)^7Q(x)[/tex]

a) Show that [tex]P(b)=P ' (b)=0[/tex]

b) Hence find a and b, if [tex](x-1)^7[/tex] is a factor of: [tex]P(x)=x^7+3x^6+ax^5+x^4+3x^3+bx^2-x-1[/tex]

2. Relevant equations

If [tex]P(x)=Q(x)R(x)[/tex]

Then [tex]P ' (x)=Q ' (x)R(x)+Q(x)R ' (x)[/tex]

I can't think of anything for the factoring aspect of the question.

3. The attempt at a solution

For a)

[tex]P(b)=(b-b)^7Q(b)=0[/tex]

[tex]P ' (x)=7(x-b)^6Q(x)+(x-b)^7Q'(x)[/tex]

[tex]P'(b)=7(b-b)^6Q(b)+(b-b)^7Q'(b)=0[/tex]

But for b) I have no idea how to apply anything from a) to answer the question. Any ideas?

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# Homework Help: Polynomial factor help

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