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# How do you write a polynomial of least degree with integral coeffients that has 5, -3 as zeros?

Mar 8, 2018

$y = {x}^{2} - 2 x - 15$

#### Explanation:

$\text{given a polynomial with zeros "x=a" and } x = b$

$\text{then "(x-a)" and "(x-b)" are it's factors}$

$\text{the polynomial can then be expressed as}$

$y = k \left(x - a\right) \left(x - b\right) \leftarrow \textcolor{b l u e}{\text{k is a multiplier}}$

$\text{here "x=5" and } x = - 3$

$\Rightarrow \left(x - 5\right) \text{ and "(x+3)" are the factors}$

$\Rightarrow y = k \left(x - 5\right) \left(x + 3\right)$

$\text{let k = 1 and expand factors}$

$\Rightarrow y = {x}^{2} - 2 x - 15 \leftarrow \textcolor{b l u e}{\text{is a possible polynomial}}$