# Finding a polynomial with given roots, degree, and specific coefficient

Find a degree 4 polynomial having zeros -6, -3, 2 and 6 and the coefficient of $x^4$ equal 1

The first step is something like $p(x)=c(x-6)(x+3)(x-2)(x-6)$ as those are all the 4 zeros.

The coefficient of $x^4$ equal to 1 is throwing me off though.

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Welcome to MathSE. I see that this is your first question. So I wanted to let you know a few things about MathSE. We like to know the sources of questions (context helps give the answer at an appropriate level). It's also important to use some tag in addition to [homework]. Please let us know what you've tried on a problem. These sort of pleasantries usually result in more and better answers. Thank you –  Arturo Magidin Nov 5 '11 at 4:54
Try multiplying out your polynomial, treating $c$ as an unknown constant for now. What does the coefficient of $x^4$ become? How can you make it $1$ by choosing $c$ appropriately? –  Henning Makholm Nov 5 '11 at 4:57

You are almost right and almost done. That first factor should be $x+6$, not $x-6$ (which you have twice). Any value of $c\neq 0$ will give you a polynomial with the roots in the right place.
And when you multiply out what you have, $$c(x+6)(x+3)(x-2)(x-6) = cx^4 + (\text{lower terms}).$$ So if you want the coefficient of $x^4$ to be $1$, then $c$ should be...
You have it correct, just change the minus to plus on the first (x-6) term and set c=1, multiplying the expression out would give you: $x^4+...$ which is what you need