Question

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

Answer 1

`-5x^2 -8x +2`

Explanation:

Standard form of polynomial equation of `2^(nd)` order is
`ax^2+bx+c`

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

`2-11x^2-8x+6x^2 = 2+(- 11x^2+6x^2) -8x`
`= 2 -5x^2-8x = -5x^2 -8x +2`

Answer 2

`-5x^2-8x+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:

`2-11^2-8x+6x^2`

Simplify `-11^2+6x^2`.

`2-5x^2-8x`

Rearrange the terms from greatest to least exponent.

`-5x^2: "exponent of"` `2`

`-8x":` `"exponent of"` `1`

`2":` `"exponent of"` `0`

`-5x^2-8x+2`

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

Answer 3

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

Explanation:

`f(x) = 2-11x^2-8x+6x^2`

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

`f(x) =(-11+6)x^2-8x+2`

`=-5x^2-8x+2`

The degree of the polynomial is the highest power of `x`. In this case `x^2`.

`:. f(x)` is a polynomial of degree 2

`f(x)` has three terms. `[-5x^2, -8x, +2]`

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