A square of an integer is the integer. Find the integer.

A square of an integer is the integer. Find the integer.
Let the integer be n. The square means we raise n to the power of 2, so we have:
n^2 = n
Subtract n from each side:
n^2 - n = n - n
n^2 - n = 0
Factoring this, we get:
n(n - 1) = 0
So n is either [B]0 or 1[/B].

Factoring and Root Finding

This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

Greatest Common Factor and Least Common Multiple

Given 2 or 3 numbers, the calculator determines the following:

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other

The product of two positive numbers is 96. Determine the two numbers if one is 4 more than the other.
Let the 2 numbers be x and y.
We have:
[LIST=1]
[*]xy = 96
[*]x = y - 4
[/LIST]
[U]Substitute (2) into (1)[/U]
(y - 4)y = 96
y^2 - 4y = 96
[U]Subtract 96 from both sides:[/U]
y^2 - 4y - 96 = 0
[U]Factoring using our quadratic calculator, we get:[/U]
(y - 12)(y + 8)
So y = 12 and y = -8. Since the problem states positive numbers, we use [B]y = 12[/B].
Substituting y = 12 into (2), we get:
x = 12 - 4
[B]x = 8[/B]
[B]We have (x, y) = (8, 12)[/B]