Find a polynomial function [Solved!]

X

Find a polynomial function with degree 3 with real coefficients that has the given zeros:
-2, 3, -4
The polynomial function is x^(3)+?x^(2)-10x-24

Relevant page

<a href="/equations-of-higher-degree/1-polynomial-functions.php">1. Polynomial Functions and Equations</a>

What I've done so far

Gone through your examples, but cannot find on e like it.

X

Hi Samantha

These pages have lots of useful background for you:

<a href="/equations-of-higher-degree/3-how-factor-polynomials.php">How to factor polynomials</a>

<a href="/equations-of-higher-degree/4-roots-polynomial-equations.php">Roots of Polynomial equations</a>

The first example in the second link is very similar to what you need to do (but the other way round).

Show us your working (you are encouraged to use the math entry system).

X

Is this what you're supposed to do?

`(x-2)(x + 3)(x -4)`

`=(x-2)(x^2-x-12)`

`=x^3-x^2-12x-2x^2+2x+24`

`=x^3-3x^2-10x+24`

So the ? mark is supposed to be `-3`, right?

X

Hi Samantha

You almost got it, but fell into a common trap. Notice your `24` at the end is `+24`, but the question says `-24`?
 
If the <b>zeros</b> (aka "roots") are `-2, 3` and `4`, then the linear parts of the factored polynomial will use opposite signs, like this:

`(x+2)(x - 3)(x +4)`

`=(x+2)(x^2+x-12)`

`=x^3+x^2-12x+2x^2+2x-24`

`=x^3+3x^2-10x-24`

So the ? mark should be `3`, not `-3`.

Hope it helps.

X

Great. I got it now.

Thanks a lot.