## Standard Form

Table of Contents

## Definition

What is “Standard Form”?

It depends on what you are dealing with!

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:

4321 = 4.321 × 10^{3}^{}

In this example, 4321 is written as 4.321 × 10^{3},

because 4321 = 4.321 × 1000 = 5.3266 × 10^{3}

In other countries it means “**not in expanded form**“:

Standard Form | Expanded Form |

4321 | 4000+300+20+1 |

## 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.

Put x^{2} = -4 into Standard Form

Answer:

x^{2} + 4 = 0

## Standard Form of a Polynomial

The *Standard Form* of polynomial is to put the terms with the highest degree first (like the “2” in x^{2} if there is one variable).

Put 5 + 3x^{2} − 2x + 4x^{3} + x^{4} in Standard Form:

The highest degree is 4, so that goes first, then 3, 2 and then the constant last:

x^{6} + 4x^{3} + 3x^{2} − 2x + 5

## Standard Form of a Linear Equation

The *Standard Form* of Linear Equation is

Ax + By = C

Where:

A > 0

A, B ≠ 0

A, B and C should be integers

Put y = 4x + 7 in Standard Form:

Bring 4x to the left:

−4x + y = 7

Multiply all by −1:

4x − y = −7

A = 4, B = −1, C = −7

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* of Quadratic Equation is

Standard Form of a Quadratic Equation:

*a*x^{2}* + bx + c* = 0

Where *a **≠** *0

Put x(x+1) = -4 in Standard Form:

First, expand x(x-1):

x^{2} + x = -4

Bring 4 to left:

x^{2} + x + 4 = 0

Note: a = 1, b = 1, c = 4