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

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Answer 1 · 2017-06-22T08:33:28

See 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:

It is a polynomial of third degree; this can be said because the highest degree of the variable $x$ with non-zero coefficient is $3$
The polynomial has four terms.

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 + 2x12x^3 - 9x^2 + 5x^3 - 6x^2 + 3 + 2x?