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Find an equation for a least-degree polynomial that has zeros at −2, 3, and 4, and y-intercept of 24.

 Feb 26, 2021
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If we have a polynomial with variable $x$, we can write the polynomial in factored form given its roots. Therefore, we get 

$$(x-(-2))(x-3)(x-4).$$ When we expand this out, we get $$x^3-5x^2-2x+24.$$ When we look at the other condition in the problem, we must have an $y$-intercept with a value of $24$. The $y$-intercept is where $x=0$, so we just look at the constant term in our polynomial and see that it is $24$. Thus, the least degree polynomial is $\boxed{x^3-5x^2-2x+24}.$

 Feb 26, 2021

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