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Find a polynomial f(x) with leading coefficient 1 and having the given degree and zeros.

Each polynomial should be expanded from factored form, simplified and written in descending order of exponents on the variable.
For example: (x+5)(x-2) should be given as the answer x^2 + 3x - 10

degree 4; zeros -3, 1, 3, 5

• math -

X = -3, X+3 = 0.

X=1, X-1 = 0.

X=3, X-3 = 0.

X=5, X-5 = 0.

(X+3)(X-1)(X-3)(X-5)= 0,
(X^2+2X-3)(X^2-8X+15) = 0,

X^4-8X^3+15X^2+2X^3-16X^2+30X-3X^2+24X-45,
Combine like-terms and get:
X^4-6X^3-4X^2+54X-45 = 0.

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