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Browse Middle School Factoring Expressions
Stars indicate particularly interesting answers or good places to begin browsing.

Factoring just numbers?
Try Middle School Factoring Numbers.

Dividing with Algebra [3/25/1996]
I need help factoring and reducing this problem: (3x-9)/(2x-6)=? and (x2+2xy)/ 3x+6y)=?

Explaining Algebra Concepts and FOIL [08/04/1998]
Some ideas for learning algebra that may help prevent frustration.

Factoring Examples [12/16/1996]
How do you factor x(x+1)(x-4) + 4(x+1)? (and other similar examples).

Factoring in the Face of the Quadratic Formula [02/25/2014]
A teen who already solves quadratics with the quadratic formula wonders why we bother learning to factor. Doctor Peterson outlines several motivations that make the skill worthwhile.

Factoring Polynomials [11/07/2001]
Factoring polynomials like 12x^3y^9 + 20x^5y^4.

Factoring Polynomials [11/16/1994]
I need an easy method for understanding factoring polynomials, especially with exponents, and also quadratic equations.

Factoring Quadratics Without Guessing [05/28/2002]
When factoring quadratic equations, do you always have to use guess and check, or is there another way to do it?

Factoring Rules [6/28/1996]
Is there a clear set of factoring rules or procedures?

Factorization by Decomposition and the Distributive [04/24/2015]
An adult familiar with how to factor a quadratic with leading coefficient other than one wonders why the technique works. Doctors Rick and Peterson reveal the proportional reasoning behind it all.

How to Factor [7/25/1996]
I have forgotten how to factor - could you give me an example and an explanation?

Solving for X [5/14/1996]
Please show me each step to solving X in the equation X^2 - 7X + 10 = 0.

Solving Quadratic Equations [2/15/1996]
A student asks for help in solving quadratic equations by factoring.

Two Methods of Factoring Quadratics [04/14/1998]
Could you describe how to factor quadratic trinomials?

What is Factoring? [01/17/1998]
How do you factor x^2 + 5x + 4 ?

Algebra: Factoring Fractions [07/30/1997]
Question: 8ab/4a2-b2 divided by 16b2/8a2-4ab.

Algebra for Equivalence [11/12/2011]
A teacher's warning about algebraic manipulations troubles a student. With simple examples, Doctor Peterson shows how dividing by a variable may destroy solutions, how taking roots may introduce extraneous ones, and how factoring makes both more explicit, all while emphasizing caution with assumptions.

Are Binomial Factors Unique? [04/22/2003]
Let's say I factor x^2 - 5x + 6 into (x-2)(x-3). Is it possible that it could be factored another way as well, using numbers other than 2 and 3?

Cancelling Algebraic Fractions [11/11/2002]
I don't understand how to cancel algebraic fractions.

Completing the Square: How Does it Work? [01/20/1999]
Can you explain why completing the square works? How exactly do you do it?

Difference between Two Cubes [11/09/2001]
Factoring a^3 - b^3.

Difference of Squares of Two Integers [7/2/1996]
Which positive integers can be written as the difference of the squares of two integers?

Difference of Two Squares [09/04/2002]
I understand how to get the difference of two squares but how would you get the equation when you have the answer?

The Discriminant of Quadratic Equations [08/06/1998]
Can you explain more about the discriminant, b^2 - 4ac? Why is it sometimes represented by a triangle (delta)?

Distributive Double Duty [04/05/2016]
A teen seeks to solve a single-variable equation without computing the common denominator of its many fractions. Doctor Greenie reveals a pattern and provides a shifty hint, then applies the distributive property twice to easily deduce the solution.

Equations and Factoring [2/5/1996]
Solve. Identify all double roots: 2(r^2 + 1)=5r

Factor 6x^2 + 12x [06/23/2003]
Factoring as finding things in common.

Factor and Multiply to Check [5/21/1996]
Is x to the second power plus 6x plus 5 factorable?

Factor and Simplify [4/10/1996]
How would you simplify the following problem? (1/x^2- 1/y^2)/(1/x^2+2/xy+1/y^2)

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 [9/5/1995]
How do I solve x^2+x-12 = 0?

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 Difference of Squares with Terms That Are Not Monomials [10/26/2008]
How can I factor something like (3x + 2)^2 - (x - 4)^2 using the formula for a difference of squares? I'm confused because the expressions being squared are not monomials.

Factoring a Fifth-Degree Polynomial [08/15/2002]
Simplify: x^5+x^4-4x^3-4x^2 over x^5+4x^4+4x^3.

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 an Equation [11/13/1995]
From 7y^3 + 14y^2 - 7y, I can factor out the 7y to get 7y(y^2 + 7y - 1). Can I factor any further?

Factoring an Equation [3/11/1996]
If you have the equation: x^2 * 2x+3 = 0, how do you factor it?

Factoring an Expression [8/5/1996]
How can I factor x^10+x+1?

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