# Find a nonzero polymonial function. The given zeros are: a) 0,

Find a nonzero polymonial function. The given zeros are:
a) 0, 1, 9
b) -3, -1, 0, 1, 3

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Alara Mccarthy
Use the formula:
$$\displaystyle{f{{\left({x}\right)}}}={\left({x}-{a}\right)}{\left({x}-{b}\right)}{\left({x}-{c}\right)}\ldots$$
Where the letters beside x are the zeros. Substitute:
a) $$\displaystyle{f{{\left({x}\right)}}}={\left({x}-{0}\right)}{\left({x}-{1}\right)}{\left({x}-{9}\right)}$$
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}-{10}{x}^{{2}}+{9}{x}$$
b) $$\displaystyle{f{{\left({x}\right)}}}={\left({x}+{3}\right)}{\left({x}+{1}\right)}{\left({x}\right)}{\left({x}-{1}\right)}{\left({x}-{3}\right)}$$
$$\displaystyle{f{{\left({x}\right)}}}={\left({x}^{{2}}-{9}\right)}{\left({x}^{{2}}-{1}\right)}{\left({x}\right)}$$
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{5}}-{10}{x}^{{3}}+{x}$$