Practice for Swapnil!

Algebra Level 4

If a polynomial \(p(x)\),when divided by \((x-a)\),leaves a remainder of \(b\),and when divided by \((x-c)\),leaves a remainder of \(z\), then what is the remainder when \(p(x)\) is divided by \((x-a)(x-c)\),if the answer is of the form,\[\dfrac{b(p-c)+z(a-p)}{a-c}\], then what is the value of \(p\)?

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