Math question help

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leafblaze

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So, I have a decent understanding of polynomial functions (math 30) but I'm struggling to get this question. Just looking to see if anyone can help me out, tytytyty

"The polynomial P(x) = x^3 + bx^2 + cx -1 has a remainder of 39 when divided by (x-4) and a remainder of -1 when divided by (x+1). Determine the values of b and c."

EDIT: I kinda figured it out but I don't really understand why it works.
 
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