Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `5-4x^2+6-11x^2`?

Answer 1

`-15x^2+11`

Explanation:

This polynomial can be simplified by collecting ' like terms'

`color(blue)(5)-color(red)(4x^2)+color(blue)(6)-color(red)(11x^2)=-15x^2+11`

This polynomial has 2 terms, `-15x^2" and" +11`

To express a polynomial in 'standard form' , we start with the highest power of the variable followed by terms with
decreasing powers until the last term, usually a constant.

The polynomial in standard form is `-15x^2+11`

The `color(blue)"degree of a polynomial"` is the value of the highest power of the variable within the polynomial. In this case `x^2` has a power value of 2.

`rArr" this polynomial is of " color(blue)"degree 2"`

In conclusion:

`5-4x^2+6-11x^2" can be simplified to " -15x^2+11`

Which is in standard form, having 2 terms and of degree 2.