Question 975001
Any cubic polynomial with roots -2,3,6 will be of this form


{{{k(x+2)(x-3)(x-6)}}}


where k is some constant


Let's expand out the polynomial



{{{k(x+2)(x-3)(x-6)}}}



{{{k(x+2)(x^2-9x+18)}}}



{{{k(x(x^2-9x+18)+2(x^2-9x+18))}}}



{{{k(x^3-9x^2+18x+2x^2-18x+36)}}}



{{{k(x^3-7x^2+36)}}}



{{{k*x^3-7kx^2+36k}}}



The x^2 term is {{{-7kx^2}}}



We want the x^2 coefficient to be -14, so, {{{-7k=-14}}} which means {{{k = 2}}}



Since k = 2, {{{k*x^3-7kx^2+36k}}} turns into {{{2x^3-14x^2+72}}} after k is replaced with 2 and you simplify


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