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.

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

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).

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?

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.