Question 997890
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For starters, if *[tex \Large f(0)\ =\ 5] then *[tex \Large d\ =\ 5].  If *[tex \Large \alpha] is a zero of a polynomial, then *[tex \Large x\ -\ \alpha] is a factor of the polynomial.  For any given polynomial *[tex \Large a_0x^n\ +\ a_1x^{n-1}\ +\ a_2x^{n-2}\ +\ ...\ +\ a_{n-1}x\ +\ a_n], all polynomials of the form *[tex \Large k\left(a_0x^n\ +\ a_1x^{n-1}\ +\ a_2x^{n-2}\ +\ ...\ +\ a_{n-1}x\ +\ a_n\right)] have the same set of zeros.


So you need to multiply the three factors *[tex \Large (x\ -\ 1)(x\ -\ 2)(x\ -\ 3)] and then find the appropriate value of *[tex \Large k] so that the constant term is equal to 5.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \