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

Question
Polynomials asked 2021-01-08
Write the simplest polynomial function with the given roots. 1, 1, 2.

## Answers (1) 2021-01-09
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
$$x^{3}-4x^{2}+5x-2$$

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