Given zeros: 1, 1, and 2.

Factor theorem states thates that if r is a zero, x-r is a factor.

\((x-1)(x-1)(x-2)\)

Foil, the first two factors

\((x^{2}-x-x+1)(x-2)\)

Simplify

\((x^{2}-2x+1)(x-2)\)

Multiply. Distribute \(x^{2}\) first, then -2x, and 1

\(x^{3}-2x^{2}-2x^{2}+4x+x-2\)

Simplify

\(x^{3}-4x^{2}+5x-2\)

Factor theorem states thates that if r is a zero, x-r is a factor.

\((x-1)(x-1)(x-2)\)

Foil, the first two factors

\((x^{2}-x-x+1)(x-2)\)

Simplify

\((x^{2}-2x+1)(x-2)\)

Multiply. Distribute \(x^{2}\) first, then -2x, and 1

\(x^{3}-2x^{2}-2x^{2}+4x+x-2\)

Simplify

\(x^{3}-4x^{2}+5x-2\)