How do you write a polynomial in standard form, then classify it by degree and number of terms $14 x^{2} - 8 + 5 x - 6 x^{2} + 2 x$ $14x^2 - 8 + 5x - 6x^2 + 2x$ ?

Question

How do you write a polynomial in standard form, then classify it by degree and number of terms $14 x^{2} - 8 + 5 x - 6 x^{2} + 2 x$ $14x^2 - 8 + 5x - 6x^2 + 2x$ ?

1 Answer

Impact of this question

5416 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-18T01:27:08

standard form: $8 x^{2} + 7 x - 8 = 0$ $8x^2+7x-8=0$
number of terms: $3$ $3$
degree of polynomial in standard form: $2$ $2$

Explanation:

Determining the Standard Form of the Polynomial
Notice how your equation follows the general equation of a quadratic function in standard form, $a x^{2} + b x + c = 0$ $color(blue)(ax^2+bx+c=0)$ . Assuming that the given equation is equal to $0$ $0$ , start by grouping all like terms and simplifying.

$14 x^{2} - 8 + 5 x - 6 x^{2} + 2 x = 0$ $14x^2-8+5x-6x^2+2x=0$

$14 x^{2} - 6 x^{2} + 5 x + 2 x - 8 = 0$ $14x^2-6x^2+5x+2x-8=0$

$color(green)(|bar(ul(color(white)(a/a)8x^2+7x-8=0color(white)(a/a) |)))$

Determining the Number of Terms
The number of terms of the polynomial in standard form can be found by first defining what a term is. A $color(red)("term")$ is a single number, a variable, or a number and variable multiplied together.

For example (but not limited to):

Single numbers: $3, 56, 623, 6134, 23980$
Variables: $x, r, u, a, f$
Number and variable: $3x, 56r, 623u, 6134a, 23980f$

Going back to your equation, the terms would be the following, where the positive and negative signs are ignored:

$underbrace(8x^2)_color(red)("term")+underbrace(7x)_color(red)("term")-underbrace(8)_color(red)("term")=0color(white)(X),color(white)(X)$ thus:

$color(green)(|bar(ul(color(white)(a/a)"number of terms"=3color(white)(a/a)|)))$

Determining the Degree
To determine the degree, take the $color(darkorange)("exponent of each variable")$ of every $color(red)("term")$ in the equation. The highest exponent out of all the terms is the degree of the polynomial.

$underbrace(8x^2)_color(red)("term")+underbrace(7x)_color(red)("term")-underbrace(8)_color(red)("term")=0$

$8x^color(darkorange)2color(teal)(->)color(darkorange)2$
$7x^color(darkorange)1color(teal)(->)color(darkorange)1$
$8color(teal)(->)0$

As you can see, the highest exponent is $2$ , so the degree of the polynomial is $2$ . The degree of the polynomial in standard form is written mathematically as:

$color(green)(|bar(ul(color(white)(a/a)"deg"(8x^2+7x-8)=2color(white)(a/a)|)))$

Science

Math

Humanities

... and beyond

How do you write a polynomial in standard form, then classify it by degree and number of terms $14 x^{2} - 8 + 5 x - 6 x^{2} + 2 x$ $14x^2 - 8 + 5x - 6x^2 + 2x$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you write a polynomial in standard form, then classify it by degree and number of terms 14x^2 - 8 + 5x - 6x^2 + 2x14x2−8+5x−6x2+2x14x^2 - 8 + 5x - 6x^2 + 2x?

1 Answer

Explanation:

Related questions

Impact of this question

How do you write a polynomial in standard form, then classify it by degree and number of terms $14 x^{2} - 8 + 5 x - 6 x^{2} + 2 x$ $14x^2 - 8 + 5x - 6x^2 + 2x$ ?