See also the
Dr. Math FAQ:
order of operations
Browse High School Basic Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Solving simple linear equations.
Positive/negative integer rules.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- Polynomial Degrees and Definition of a Field [03/02/1998]
The degree of polynomials added together, and definition of a field.
- Polynomial Factoring Rules [04/02/1997]
How do I apply the polynomial factoring rules to t^21+1 and 25y^2-144 =
- Polynomial Problem [3/11/1995]
A remainder of 9 results when the polynomial p(x) is divided by x-2, a
remainder of -3 when p(x) is divided by x+2, and a remainder of 3 when
divided by x-1. Find the remainder when p(x) is divided by (x-2)(x+2)(x-
- Population and Percentage [03/07/1999]
Given population data, find the number of women in two different years.
- Positive Unit Fractions [10/02/2002]
Find five different positive unit fractions whose sum is 1. (A unit
fraction is a fraction whose numerator is 1. All denominators must
also be natural numbers.)
- Precedence of Unary Operators [09/01/99]
The PEMDAS rule for order of operations ignores unary operators. Can you
explain the proper precedence for them, and give an example showing how
not knowing the rule can cause an incorrect result?
- Preparing for an Algebra Test [11/1/1995]
A 9th grade math student asks for help preparing for final exams. What is
the difference between the terms: solve and simplify? How do you find the
gradient in a graph?
- Prize Money [09/04/1997]
If first prize wins $1,000 out of $6,000 and twentieth prize wins $100,
how much money do second through nineteenth place win? Is this a
- Probability of a Function Having Complex Roots [05/11/2000]
What is the probability that the function f(x) = x^2 + px + q = 0 will
have complex roots when p and q lie between 0 and 1? ...when p and q lie
between 0 and 5? ...when p and q are greater than 0?
- Probate Puzzle [12/15/2003]
A will specifies that every son should receive three times as much as
a daughter and every daughter should get two times as much as their
mother. What is the mother's share?
- Proof of Convergence [09/29/2000]
Why does the ratio F(n+1)/F(n) for the Fibonacci numbers converge to the
- Proof of the Rational Root Theorem [11/13/2000]
How can I prove the Rational Root theorem?
- Proof That 3 = 0? [10/28/2006]
Starting with x^2 + x + 1 = 0 and using algebraic manipulations, I
seem to be showing that 3 = 0. Where am I going wrong?
- Proof That All Numbers Are Equal? [12/06/2005]
I saw a proof that all numbers are equal, which makes math pointless.
There must be something wrong with the proof. Can you tell me what?
- Proof That Equation Has No Integer Roots [05/09/2000]
How can I prove that if p is a prime number, then the equation x^5 - px^4
+ (p^2-p)x^3 + px^2 - (p^3+p^2)x - p^2 = 0 has no integer roots?
- Proof Using Pell's Equation [09/18/1999]
Given Pell's equation for sqrt(D) and p/q = [a1;a2;...;an], can you prove
that p^2 - D.q^2 = (-1)^n.k?
- Proof with Inequalities [10/10/1999]
1. How can I prove that a^6 + 4*b^6 >= 4 if ab = 1? 2. At each vertex of
a polygon, a number is written... How many sides does the polygon have?
- Prove Triangle of Sides with Length... [8/1/1996]
Let a, b and c be the lengths of the sides of a triangle. Prove that the
square root of (a+b-c) plus the square root of (b+c-a) plus the square
root of (c+a-b) is equal to or less than the sum of the square roots of
a, b and c. Determine when equality occurs.
- Pumpkin Price [06/28/2001]
Peter Peter has 40 pumpkins to sell. He will sell them all if he sets his
price at $1.00 each, but will sell one fewer pumpkin for each 5-cent
increase in price...
- Quadratic Equation [6/22/1996]
What is a quadratic equation used for?
- Quadratic Equation [8/28/1996]
What is the formula for the quadratic equation?
- Quadratic Equation [04/08/1997]
The sum of two numbers is 15 and their product is 54. Find the numbers...
- Quadratic Formula [10/01/1999]
Could you give me some ideas for how to use the quadratic formula, and
some practice problems?
- The Quadratic Formula [12/12/2005]
We've been studying the quadratic formula as a way to solve quadratic
equations, but I'm a little confused by it. Can you give me a summary
of what the formula is, how and when you apply it, and why it's important?
- Quadratic Formulas, Equations, Parabolas, Graphing [6/16/1996]
Given 6x^2 + x - 1 = 0, how do I find the roots, the vertex, some
coordinates, and from these graph it?
- Quadratic Formula: Solve for b [08/15/2001]
How do you solve for b in the quadratic formula?
- Quadratic Function [05/04/2001]
What are the effects of changing the values of a, b, and c in a quadratic
- Quadratic Inequalities [03/18/2003]
When I solve (x^2 + 1)/4 greater than or equal to (x + 2)/2 , of my
final two answers, only one works.
- A Quadratic Inequality [4/27/1996]
Solve the inequality: (3x+1)(5-10x)>0
- Quadratic Model [12/03/2001]
The quadratic model S = -17t^2+45t+2570 approximates the number of
suicides by firearms in the U.S. for women, where t represents the number
of years after 1985. In what year were there 2370 female suicides by
- Quadratic Problem [7/12/1995]
Find the quadratic functions with vertex (3,-1) and one x-intercept at
- Quadratic Trinomials [8/14/1995]
How do you factor quadratic trinomials as the product of linear
- Quadrilateral Patterns [03/06/1997]
What is the formula that gives the number of quadrilaterals within a
square grid when you increase the square grid by one unit on each side?
- Quarter Circles [12/20/1996]
Find a function that graphs a quarter of a circle in quadrants II and IV.
- Radical Equation [04/12/1997]
How do I solve the radical equation 3x+(5x^(1/2))-28=0?
- Radioactive Decay of an Isotope [01/05/1998]
I know the decay of the 226Ra isotope involves the use of logarithms (an
exponential function ae^x), but I'm having trouble fitting my information
to my equation...
- Raising Sides of an Equation to the 0 Power [12/04/1997]
If you raise both sides of an equation to the 0 power, will both sides
then be equal to one?
- Raising Sqrt(2) [10/14/1997]
What is the value of x in the following equation: x^x^x^x^x ... = 2 ?
- Rate of River Current [10/31/2001]
Ryan is canoeing upstream while his sister Katie sleeps in the back of
- Rates of Paddling [04/25/2000]
I can travel 12 miles downstream in six hours less than it takes me to
travel the same distance upstream... How fast is this river's current?