How do you write a polynomial in standard form, then classify it by degree and number of terms #12x^3 - 9x^2 + 5x^3 - 6x^2 + 3 + 2x#?

1 Answer
Jun 22, 2017

See explanation.

Explanation:

The starting polynomial is:

#12x^3-9x^2+5x^3-6x^2+3+2x#

The standard form means sorting the polynomial by the decreasing degree of terms:

#12x^3+5x^3-9x^2-6x^2+2x+3#

Now we can combine the like terms:

#12x^3+5x^3=17x^3#

#-9x^2-6x^2=-15x^2#

After the operation the polynomial is:

#17x^3-15x^2+2x+3#

The polynomial is now in the standard form. From the form we can say that:

  1. It is a polynomial of third degree; this can be said because the highest degree of the variable #x# with non-zero coefficient is #3#

  2. The polynomial has four terms.