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 × 103
In this example, 4321 is written as 4.321 × 103,
because 4321 = 4.321 × 1000 = 5.3266 × 103
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 x2 = -4 into Standard Form
Answer:
x2 + 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 x2 if there is one variable).
Put 5 + 3x2 − 2x + 4x3 + x4 in Standard Form:
The highest degree is 4, so that goes first, then 3, 2 and then the constant last:
x6 + 4x3 + 3x2 − 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:
ax2 + bx + c = 0
Where a ≠ 0
Put x(x+1) = -4 in Standard Form:
First, expand x(x-1):
x2 + x = -4
Bring 4 to left:
x2 + x + 4 = 0
Note: a = 1, b = 1, c = 4