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1. Using factor theorem, show that \((x - 5)\) is a factor of the polynomial \(2x^3 - 5x^2 - 28x + 15\).
Answer:
\(p(5) =\)
Therefore, \((x - 5\)) is of the polynomial \(2x^3 - 5x^2 - 28x + 15\).
2. Determine the value of \(m\), if \((x + 3)\) is a factor of \(x^3 - 3x^2 - mx + 24\).
Answer:
\(m =\)
3. If \((x - 1)\) divides the polynomial \(kx^3 - 2x^2 + 25x - 26\) without remainder, then find the value of \(k\).
Answer:
\(k =\)
4. Check if \((x + 2)\) and \((x - 4)\) are the sides of a rectangle whose area is \(x^2 - 2x - 8\) by using factor theorem.
Answer:
Let \(p(x) = x^2 - 2x - 8\)
\(p(-2) =\)
\(p(4) =\)
Therefore, \((x + 2)\) and \((x - 4)\) are of a rectangle.
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