Write the simplest polynomial function with the given roots 1, 4, and 3?

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Answer 1 · 2018-05-14T15:08:18

$p (x) = (x - 1) (x - 4)$ $p(x)=(x-1)(x-4)$ $(x - 3)$ $(x-3)$

Answer 2 · 2018-05-14T15:11:21

$y = x^{3} - 8 x^{2} + 19 x - 12$ $y = x^3-8x^2+19x-12$

A polynomial with roots, 1, 4, and 3 will have the factored form:

$y = (x - 1) (x - 4) (x - 3)$ $y = (x-1)(x-4)(x-3)$

Multiply the last two factors:

$y = (x - 1) (x^{2} - 7 x + 12)$ $y = (x-1)(x^2-7x+12)$

Distribute the first factor over the second:

$y = x (x^{2} - 7 x + 12) - 1 (x^{2} - 7 x + 12)$ $y = x(x^2-7x+12)-1(x^2-7x+12)$

Multiply:

$y = x^{3} - 7 x^{2} + 12 x - x^{2} + 7 x - 12$ $y = x^3-7x^2+12x-x^2+7x-12$

Combine like terms:

$y = x^{3} - 8 x^{2} + 19 x - 12$ $y = x^3-8x^2+19x-12$