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

Feb 10, 2018

$3 {x}^{5} + 6 {x}^{4} - 12 {x}^{3} - 9 {x}^{2} - 18 x + 36$

#### 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:

$3 {x}^{3} - 9$

Next, we multiply this by the trinomial $\left({x}^{2} + 2 x - 4\right)$:

$\textcolor{red}{3 {x}^{3}} \textcolor{b l u e}{- 9} \left({x}^{2} + 2 x - 4\right)$

$= \textcolor{red}{3 {x}^{3}} \left({x}^{2} + 2 x - 4\right) \textcolor{b l u e}{- 9} \left({x}^{2} + 2 x - 4\right)$

$= \left(3 {x}^{5} + 6 {x}^{4} - 12 {x}^{3}\right) - 9 {x}^{2} - 18 x + 36$

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

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