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9514 1404 393
Answer:
p(x) = x^3 +x^2 -82x +80
Step-by-step explanation:
If a polynomial function has a zero at x=a, then (x -a) is a factor. Your list of zeros means the factors are ...
p(x) = (x -8)(x +10)(x -1) . . . . . . . . factored form
When this is multiplied out, it becomes ...
p(x) = x^3 +x^2 -82x +80 . . . . . . standard form
_____
The factored form can be multiplied out using the distributive property.
= ((x(x +10) -8(x +10))(x -1)
= (x^2 +10x -8x -80)(x -1)
= (x^2 +2x -80)x -(x^2 +2x -80)
= x^3 +2x^2 -80x -x^2 -2x +80
= x^3 +x^2 -82x +80
