# How do you write a polynomial in standard form, then classify it by degree and number of terms 2 – 11x^2 – 8x + 6x^2 ?

Oct 17, 2017

$- 5 {x}^{2} - 8 x + 2$

#### Explanation:

Standard form of polynomial equation of ${2}^{n d}$ order is
$a {x}^{2} + b x + c$

Rearrange the like terms together and then simplify. Then arrange then again rearrange them in the standard format given above.

$2 - 11 {x}^{2} - 8 x + 6 {x}^{2} = 2 + \left(- 11 {x}^{2} + 6 {x}^{2}\right) - 8 x$
$= 2 - 5 {x}^{2} - 8 x = - 5 {x}^{2} - 8 x + 2$

Oct 17, 2017

$- 5 {x}^{2} - 8 x + 2$

The polynomial has three terms (separated by $+$ and $-$ signs), and a degree of $2$ because the largest exponent is $2$.

#### Explanation:

Write in standard form:

$2 - {11}^{2} - 8 x + 6 {x}^{2}$

Simplify $- {11}^{2} + 6 {x}^{2}$.

$2 - 5 {x}^{2} - 8 x$

Rearrange the terms from greatest to least exponent.

$- 5 {x}^{2} : \text{exponent of}$ $2$

-8x":$\text{exponent of}$ $1$

2":$\text{exponent of}$ $0$

$- 5 {x}^{2} - 8 x + 2$

The polynomial has three terms (separated by $+$ and $-$ signs), and a degree of $2$ because the largest exponent is $2$.

Oct 17, 2017

$- 5 {x}^{2} - 8 x + 2$
A polynonial of degree 2 with 3 terms also known as a "quadratic function"

#### Explanation:

$f \left(x\right) = 2 - 11 {x}^{2} - 8 x + 6 {x}^{2}$

Combine like powers of $x$ and order terms accordingly.

$f \left(x\right) = \left(- 11 + 6\right) {x}^{2} - 8 x + 2$

$= - 5 {x}^{2} - 8 x + 2$

The degree of the polynomial is the highest power of $x$. In this case ${x}^{2}$.

$\therefore f \left(x\right)$ is a polynomial of degree 2

$f \left(x\right)$ has three terms. $\left[- 5 {x}^{2} , - 8 x , + 2\right]$

NB: Such a function is also known as a "quadratic" (from the Latin word for square "quadratum")