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.
- Extraneous Roots Checked Less Tediously [06/06/2012]
A student seeks an expedient way to check unwieldy solutions for extraneous roots.
Doctor Peterson first considers their source, then offers a quick check method, and
finally recommends using a calculator with memory function.
- Extraneous Routes [10/02/2013]
A student seeks all the ways in which extraneous roots arise. Doctor Peterson details a
few pitfalls before emphasizing that the steps you take matter more than what you
- Extraneous Solutions [08/08/2003]
What should an engineer interpret from an equation, or the solutions
of that equation, if its solutions prove to be extraneous?
- Factor and Multiply to Check [5/21/1996]
Is x to the second power plus 6x plus 5 factorable?
- Factor Completely [02/13/1998]
The problems are: x^12-y^12 and x^12+y^12.
- Factor for X; Consecutive Odd Integers [01/19/1998]
(x-2)(x+3) = 6 : solve by factoring for x. Label your variables, write an
equation, solve, label answers...
- Factoring [12/03/2001]
This problem is giving me a hard time: 6x^2 + 31x + 5.
- Factoring 5x^2 + 2x -1 [01/22/2001]
I can't figure out how to factor this: 5x^2 + 2x -1. The best I can do
is: (5x+1)^2 + 2(x-1).
- Factoring 8 - t^3 [01/07/1998]
Factor the given expression completely: 8 - t^3.
- Factoring a 3-Variable Polynomial [08/13/1999]
Is it possible to factor the polynomial k1*x^2 + k2*y^2 + k3*z^2 + k4*xy
+ k5*xz + k6*yz into (g1*x + g2*y + g3*z)(h1*x + h2*y + h3*z) over the
complex field for every choice of k1 through k6?
- Factoring Algebraic Expressions [6/15/1996]
Factor (xy+1)(x+1)(y+1)+xy and ...
- Factoring and the Factor Theorem [09/28/1998]
I need help factoring x^3 - x^2 + x - 2 = 4.
- Factoring a Sum of Squares [10/15/2005]
I do not understand why you cannot factor a sum of two squares, but
you can factor a perfect square trinomial.
- Factoring a Trinomial [08/26/1997]
How do you reduce 5k^2-13k-6 / 5k+2 to lowest terms?
- Factoring a Trinomial [08/22/2003]
What is factoring by grouping? When factoring a trinomial, why is it
necessary to write the trinomial in four terms?
- Factoring by Grouping [05/27/1998]
How do you factor 2r^2 + rt - 6t^2 ?
- Factoring by Grouping to Solve a Polynomial Equation [05/26/2005]
How do I solve an equation like x^3 + 3x^2 - x - 3 = 0 by factoring?
I'm having trouble factoring because of the four terms and the x^3.
- Factoring Expressions [01/19/1997]
Factor 3x-21, 5x^2y-15xy^2, 18x^2-27x, and 2a-8b-10.
- Factoring Polynomials [11/29/1999]
How can I factor 4x^2 - 36, or x^2 + yz + xy + xz?
- Factoring Quadratic Equations [5/27/1996]
What's the fastest way to solve any type of quadratic equation?
- Factoring Quadratic Equations [7/22/1996]
Are there common points or rules I can apply in every situation?
- Factoring Quadratics [06/10/1997]
How do you factor 2x^2 - 11x + 15 or 6a^2 + 7a - 5?
- Factoring Quadratics When a Doesn't = 1 [03/24/2003]
A trick to solving quadratics was presented to me. I was wondering
if there is a proof for it.
- Factoring to Find the Limit [11/5/1995]
Factoring the numerator of a limit problem.
- Factoring Trinomials [05/28/1999]
How do you factor trinomials with a number in front of the first
variable? For example: 6y^2 - 19y + 10.
- Factoring Trinomials By Grouping [11/16/2004]
A discussion of using the grouping method to factor a trinomial and
how to determine the correct middle terms, as well as using the
discriminant to test if the polynomial is factorable.
- Factoring Trinomials by the Grouping Method [12/08/2005]
A discussion and proof of why factoring trinomials by grouping works.
- Factoring vs. Simplifying [03/02/2003]
Factor the expression 1+y(1+x)^2(1+xy).
- Factoring with 3 Variables [4/8/1996]
This one has been frustrating. Factor: 9a^2+4bc-4c^2-b^2
- Factoring (x - 1)(x^2 - x - 2) [11/04/1997]
I don't remember how to factor.
- Fermat's Last Theorem with Negative Exponents [10/26/2000]
Are there any solutions of Fermat's Last Theorem, x^n + y^n = z^n, for n
less than 2?
- Ferrari's Method for Quartics [04/16/1999]
Could you explain Ferrari's method for quartics?
- Find all Integer Values of x.... [6/27/1996]
Find all integer values of x for which [12(x^2-4x+3) / (x^3-3x^2-x+3)]
has a positive integer value.
- Finding a Formula for a Number Pattern [09/30/2004]
We are learning about sequences and how to find the patterns in
numbers. Our teacher gave us the sequence 0, 3, 8, 15, 24, 35 and
told us that we had to use factoring to find the answer. I know the
answer is (n + 1)(n - 1), but I can't see how to get that.
- Finding a Formula for Mixtures [11/10/2003]
Alfredo needs to make 250 ml of a 27% alcohol solution, using a 15%
solution and a 40% solution. How much of each should he use?
- Finding an Inverse Function [8/28/1996]
What is the inverse function of f(x) = 1 - 2x? What is the general method
for finding an inverse function?
- Finding a Rule to Fit Given Data [11/14/2005]
Given that 1J1 = 2, 3J5 = 34, 6J9 = 117, and 10J14 = 296, conjecture a
value for 3J8.
- Finding a Set, Solving a System [06/24/1998]
Find the solution set: 3-1/4x <_ 2+ 3/8 x; solve the system...
- Finding a Single Pair of Factors [02/27/2002]
Factor ax^2 - bx - c.
- Finding Asymptotes [07/06/1998]
In the equation y = (m/x) + c, how do the values of m and c affect the
graph? How do you find the asymptotes?