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# Anyone know how to do this problem?

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Construct a polynomial function of least degree possible using the given information.

Real roots: −1, 1, 3 and (2,f(2))=(2,5)

Oct 14, 2018

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$$\text{the polynomial will be of the form}\\ p(x) = k(x+1)(x-1)(x-3) \\ p(2) = k(3)(1)(-1) = 5 \\ -3k = 5 \\ k=-\dfrac 5 3 \\ p(x) = \dfrac 5 3 (x+1)(x-1)(x-3) \\ p(x) = -\dfrac{5 x^3}{3}+5 x^2+\dfrac{5 x}{3}-5$$

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Oct 14, 2018

$$\text{the polynomial will be of the form}\\ p(x) = k(x+1)(x-1)(x-3) \\ p(2) = k(3)(1)(-1) = 5 \\ -3k = 5 \\ k=-\dfrac 5 3 \\ p(x) = \dfrac 5 3 (x+1)(x-1)(x-3) \\ p(x) = -\dfrac{5 x^3}{3}+5 x^2+\dfrac{5 x}{3}-5$$