Ask Dr. Math

High School Archive

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.
    Mixture problems.
    Quadratic equations.
    Absolute value.
    Completing the square.
    Direct and indirect variation.
    Inequalities and negative numbers.

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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?

Finding Coefficients of Simultaneous Equations [06/24/1998]

The equations ax^4 + bx^3 + c = 0 and cx^4 + bx^3 + a = 0 have a common root. Find all possible values of b, if a + c = 100.

Finding Equations from Relations [01/06/1998]

Can you give me simple steps for how to do a chapter in the book called "Finding Equations from Relations"?

Finding Equations of Parabolas [12/12/1996]

Determine the equation of the parabola whose vertex is at (1,3) and whose directrix is y=x.

Finding Focus and Directrix [04/12/2001]

How can you find the focus and directrix when given a formula for a parabola?

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