SOLUTION: How do you write a polynomial in standard form using the given zeros 2, 5, and 4

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Question 280027: How do you write a polynomial in standard form using the given zeros 2, 5, and 4
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
Consider:
(x-a)(x-b)(x-c)=0
Recall from properties of numbers that if you multiply any quantity by 0 you get 0. So at least one of x-a, x-b, x-c has to be 0 for this to be true. What makes that true? x=a,x=b,x=c! So for your zeros we want: (x-2)(x-5)(x-4) because if the zeroes are 2,5,4 that makes respective ones zero.
So, now you just want to expand the expression:
(x-2)(x-5)(x-4)=(x^2-7x+10)(x-4)=x^3-11x^2+38x-40.