How do you write a polynomial with zeros: -3,1,5,6?

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How do you write a polynomial with zeros: -3,1,5,6?

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Answer 1 · 2016-02-04T21:13:29

For a zero, when $x$ $x$ has that value the overall bracket (parenthesis) needs to sum to zero. For example $(x + 3) = (- 3 + 3) = 0$ $(x+3)=(-3+3)=0$ . That means the solution is $(x + 3) (x - 1) (x - 5) (x - 6)$ $(x+3)(x-1)(x-5)(x-6)$ .

Explanation:

A 'zero' or 'root' of an equation is a point at which it crosses the $x$ $x$ -axis: that is, the line $y = 0$ $y=0$ (or $f (x) = 0$ $f(x)=0$ ).

For that to happen, one of the factors must go to zero. If we take the example of $x = - 3$ $x=-3$ , we need a factor that, when $x$ $x$ has that value, will equal zero. If it's in the form $(x + a)$ $(x+a)$ and we put in the value $x = - 3$ $x=-3$ , the value of $a$ $a$ required is $3$ $3$ .

For a positive value of $x$ $x$ such as $x = 5$ $x=5$ , the factor needs to be $(x - 5)$ $(x-5)$ so that it becomes zero when $x = 5$ $x=5$ .

Using this approach, over all we get:

$(x + 3) (x - 1) (x - 5) (x - 6)$ $(x+3)(x-1)(x-5)(x-6)$

We could multiply this through to get an expression in $x^{4}$ $x^4$ and all lower values, but it's probably best left in this factorized form.

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How do you write a polynomial with zeros: -3,1,5,6?

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