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The Remainder Theorem states that the remainder of the division of a polynomial $f(x)$ by a linear divisor $(x - r)$ is .
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To use the Remainder Theorem, first substitute $x = r$ into the expression $f(x)$. If $f(x) = 2x^2 + 3x + 5$ and $x = 2$, the remainder is .
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The polynomial $p(x) = x^3 - 4x^2 + 6x - 24$ when divided by $x - 2$ leaves a remainder of .
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If a polynomial $g(x)$ leaves a remainder of 0 when divided by $(x - 3)$, then $g(3)$ is .
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A factor of a polynomial $h(x)$ is $(x - 4)$ if and only if the value of $h(4)$ is .
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