# 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?

Jun 22, 2017

See explanation.

#### Explanation:

The starting polynomial is:

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

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

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

Now we can combine the like terms:

$12 {x}^{3} + 5 {x}^{3} = 17 {x}^{3}$

$- 9 {x}^{2} - 6 {x}^{2} = - 15 {x}^{2}$

After the operation the polynomial is:

$17 {x}^{3} - 15 {x}^{2} + 2 x + 3$

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.