If [tex] n \geq 1 [/tex] and [tex] f(a) = 0 [/tex] for some real(adsbygoogle = window.adsbygoogle || []).push({}); a, then [tex] f(x) = (x-a)h(x) [/tex], wherehis a polynomial of degree [tex] n-1 [/tex]. So:

[tex] f(a) = \sum_{k=0}^{n} c_{k}a^{k} = c_{0} + c_{1}a + c_{2}a^{2} + ... + c_{n}a^{n} = 0 [/tex]. In a hint it says to consider [tex] p(x) = f(x+a) [/tex]. So I expanded that and got: [tex] c_{0}+c_{1}(x+a)+c_{2}(x+a)^{2} + ... + c_{n}(x+a)^{n} [/tex]. So how do I use this to prove the above statement?

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# Homework Help: Polynomial Proofs

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