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

1 Answer
Feb 10, 2018

Answer:

#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.