Question

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.

1(multiplicity 2), -2(multiplicity 3)

*** I don't even know why multiplicity means.

Answer 1

multiplicity is how many times each root repeats
(x-r1) where r1 is the root
root is 1 of multiplicity 2 means
(x-1)^2

root -2 multiplicity 3 means
(x+2)^3

so the function is
(x-1)^2(x+2)^3
f(x)=(x-1)^2(x+2)^3
expanded
f(x)=
`x^5+4x^4+3x-10x^2-4x+8`
(x-1)^2(x+2)^3

Answer 2

To write a polynomial function of minimum degree in the standard form, you must first identify the equation and that is (x-1)^2 and (x+2)^3, then multiply it to get the standard form and the standard for for it is x^2-2x-1 and x3+6x^2+12x+16