# Find a polynomial function [Solved!]

**Samantha** 14 Dec 2015, 22:52

### My question

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

1. Polynomial Functions and Equations

### What I've done so far

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

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.

## Re: Find a polynomial function

**Murray** 16 Dec 2015, 02:00

Hi Samantha

This page has lots of useful background for you:

3. Factors and Roots of Polynomial Equations

The first example 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

Hi Samantha
This page has lots of useful background for you:
<a href="/equations-of-higher-degree/3-factors-roots.php">3. Factors and Roots of Polynomial Equations</a>
The first example 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).

## Re: Find a polynomial function

**Samantha** 17 Dec 2015, 05:27

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

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?

## Re: Find a polynomial function

**Murray** 17 Dec 2015, 15:46

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 **zeros** (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

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.

## Re: Find a polynomial function

**Samantha** 18 Dec 2015, 04:58

Great. I got it now.

Thanks a lot.

X

Great. I got it now.
Thanks a lot.

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