The polynomial function is P(x) = x³ - 3x² + 4x - 2
If the zeros of the polynomial are
then its factors are,
- x - 1,
- x - (1 + i)
- x - (1 - i)
To obtain the polynomial function, we multiply its factors together.
So, P(x) = (x - 1)(x - (1 + i)][x - (1 - i)]
= (x - 1)[(x - 1 + i)][x - 1 - i)]
= (x - 1)[(x - 1) + i)][(x - 1) - i)]
= (x - 1)[(x - 1)² - i²] (difference of two squares)
= (x - 1)[x² - 2x + 1 - (-1)]
= (x - 1)[x² - 2x + 1 + 1]
= (x - 1)[x² - 2x + 2]
= x³ - 2x² + 2x - x² + 2x - 2
= x³ - 2x² - x² + 2x + 2x - 2
= x³ - 3x² + 4x - 2
So, the polynomial function is P(x) = x³ - 3x² + 4x - 2
Learn more about polynomial function here:
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