How do you find a polynomial function that has zeros $x=-3, 1, 5, 6$ and degree n=5?

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Answer 1 · 2017-02-10T20:50:20

$=x^5-6x^4-22x^3+108x^2+189x-270$

The function could be the following:

$f(x)=(x+3)^2(x-1)(x-5)(x-6)$

that's

$=(x^2+6x+9)(x^2-6x+5)(x-6)$

$=(x^4cancel(-6x^3)+5x^2cancel(+6x^3)-36x^2+30x+9x^2-54x+45)(x-6)$

$=(x^4-22x^2-24x+45)(x-6)$

$=x^5-6x^4-22x^3+132x^2-24x^2+144x+45x-270$

$=x^5-6x^4-22x^3+108x^2+189x-270$

How do you find a polynomial function that has zeros x=-3, 1, 5, 6x=-3, 1, 5, 6 and degree n=5?