# Write the simplest polynomial function with the given roots. 1, 1, 2.

Write the simplest polynomial function with the given roots. 1, 1, 2.
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Given zeros: 1, 1, and 2.
Factor theorem states thates that if r is a zero, x-r is a factor.
$\left(x-1\right)\left(x-1\right)\left(x-2\right)$
Foil, the first two factors
$\left({x}^{2}-x-x+1\right)\left(x-2\right)$
Simplify
$\left({x}^{2}-2x+1\right)\left(x-2\right)$
Multiply. Distribute ${x}^{2}$ first, then -2x, and 1
${x}^{3}-2{x}^{2}-2{x}^{2}+4x+x-2$
Simplify
${x}^{3}-4{x}^{2}+5x-2$