Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `9x^2 – 2x + 3x^2`?

Answer 1

`12x^2-2x` is a 2nd degree polynomial.

Explanation:

The standard form of a polynomial is

`f(x)=a_0x^n+a_1x^(n-1)+a_3x^(n-2)+cdots+a_(n-1)x+a_n`

This means that in order to write a polynomial in standard form requires that the highest degree (exponent) goes the far left hand side.

In the polynomial you gave, two of the values have the same degree, the terms with the `x^2` in it.
`f(x)=color(red)(9x^2)-2x+color(red)(3x^2)`

Because these terms have the same degree, 2, you can add them
`f(x)=12x^2-2x`

Because the polynomial is now in standard form, you can determine the degree. This is a 2nd degree polynomial.