Problem

Find the equation of a polynomial given the roots are \(2\), \(-3\), and \(1\).

Answer

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Answer

Finally, we expand the expression further to get the polynomial: \((x^2 + x - 6)(x - 1) = x^3 - x^2 - 7x + 6\).

Steps

Step 1 ：Given the roots, we can express the polynomial as \((x - 2)(x + 3)(x - 1)\).

Step 2 ：Next we expand the expression: \((x - 2)(x + 3)(x - 1) = (x^2 + x - 6)(x - 1)\).

Step 3 ：Finally, we expand the expression further to get the polynomial: \((x^2 + x - 6)(x - 1) = x^3 - x^2 - 7x + 6\).

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