Question

What is the standard form of a polynomial `3(x^3-3)(x^2+2x-4)`?

Answer 1

`3x^5+6x^4-12x^3-9x^2-18x+36`

Explanation:

Polynomials are in standard form when the highest-degree term is first, and the lowest degree term is last. In our case, we just need to distribute and combine like terms:

Start by distributing the `3` to `x^3-3`. We multiply and get:

`3x^3-9`

Next, we multiply this by the trinomial `(x^2+2x-4)`:

`color(red)(3x^3)color (blue)(-9)(x^2+2x-4)`

`=color(red)(3x^3)(x^2+2x-4)color (blue)(-9)(x^2+2x-4)`

`=(3x^5+6x^4-12x^3)- 9x^2-18x+36`

There are no terms to combine, since every term has a different degree, so our answer is:

`3x^5+6x^4-12x^3-9x^2-18x+36`, a 5th degree polynomial.