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

Aug 9, 2016

$- 15 {x}^{2} + 11$

Explanation:

This polynomial can be simplified by collecting ' like terms'

$\textcolor{b l u e}{5} - \textcolor{red}{4 {x}^{2}} + \textcolor{b l u e}{6} - \textcolor{red}{11 {x}^{2}} = - 15 {x}^{2} + 11$

This polynomial has 2 terms, $- 15 {x}^{2} \text{ and} + 11$

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 $- 15 {x}^{2} + 11$

The $\textcolor{b l u e}{\text{degree of a polynomial}}$ is the value of the highest power of the variable within the polynomial. In this case ${x}^{2}$ has a power value of 2.

$\Rightarrow \text{ this polynomial is of " color(blue)"degree 2}$

In conclusion:

$5 - 4 {x}^{2} + 6 - 11 {x}^{2} \text{ can be simplified to } - 15 {x}^{2} + 11$

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