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
\(x^{3}-4x^{2}+5x-2\)
0

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