Find a polynomial that leaves the remainder $15$ when divided by $x-3$ and $2x+1$ when divided by $(x-1)^2$?
2026-03-28 22:24:49.1774736689
Problem on remainder theorem on polynomials
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We seek a polynomial such that $p(3)=15$, $p(1)=3$, and $p'(1)=2$.
If we assume $p(x)=cx^2+bx+a$, that yields three equations; can you solve them for $c$, $b$, and $a$?