# Standard Form

What is "Standard Form"?

that depends on what you are dealing with!

I have gathered some common "Standard Form"s here for you..

Note: Standard Form is **not** the "correct form", just a handy agreed-upon style. You may find some other form to be more useful.

## Standard Form of a Decimal Number

In **Britain** this is another name for Scientific Notation, where you write down a number this way:

In this example, 5326.6 is written as **5.3266 × 10 ^{3}**,

because 5326.6 = 5.3266 × 1000 = 5.3266 × 10

^{3}

In **other countries** it means "not in expanded form" (see Composing and Decomposing Numbers):

561 | 500 + 60 + 1 |

Standard Form |
Expanded Form |

## Standard Form of an Equation

The "Standard Form" of an equation is:

*(some expression)* = 0

In other words, "= 0" is on the right, and everything else is on the left.

### Example: Put x^{2} = 7 into Standard Form

Answer:

x^{2} − 7 = 0

## Standard Form of a Polynomial

The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first (like the "2" in x^{2} if there is one variable).

### Example: Put this in Standard Form:

### 3**x**^{2} − 7 + 4**x**^{3} + **x**^{6}

^{2}

^{3}

^{6}

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

**x ^{6}** + 4

**x**+ 3

^{3}**x**− 7

^{2}Also, within each term, it is nice to have the variables in alphabetical order (if it does not make things more confusing):

### Example: Put this in Standard Form:

**yzx**^{2} + 4**yx**^{3}

^{2}

^{3}

The highest degree is 3, so that goes first, also put the variables in alphabetical order

4**x ^{3}y** + 3

**x**

^{2}yz## Standard Form of a Linear Equation

The "Standard Form" for writing down a Linear Equation is

Ax + By = C

**A** shouldn't be negative, **A** and **B** shouldn't both be zero, and **A**, **B** and **C** should be integers.

### Example: Put this in Standard Form:

**y = 3x + 2**

Bring 3x to the left:

−3x + y = 2

Multiply all by −1:

3x − y = −2

Note: A = 3, B = −1, C = −2

This form:

Ax + By + C = 0

is sometimes called "Standard Form", but is more properly called the "General Form".

## Standard Form of a Quadratic Equation

The "Standard Form" for writing down a Quadratic Equation is

(**a** not equal to zero)

### Example: Put this in Standard Form:

**x(x−1) = 3**

Expand "x(x−1)":

x^{2 }− x = 3

Bring 3 to left:

x^{2} − x − 3 = 0

Note: a = 1, b = −1, c = −3

## Standard Form of a Circle Equation

With a circle like this:

The Standard Form is this:

(x−a)^{2} + (y−b)^{2} = r^{2}

See Circle Equations for more details.