Ask Dr. Math
Middle School Archive
Dr. Math Home ||
Middle School ||
High School ||
Dr. Math FAQ
See also the
Dr. Math FAQ:
learning to factor
3D and higher
Browse Middle School Factoring Expressions
Stars indicate particularly interesting answers or
good places to begin browsing.
Factoring just numbers?
Try Middle School Factoring Numbers.
- Factoring another Equation [11/14/1995]
40y squared + yz - 6z squared?
- Factoring a Quadratic Equation [05/13/1998]
Using prime factorization and FOIL method to solve y^2 + 2y - 35 = 0.
- Factoring a Quadratic with Fractions [10/08/1999]
How can I factor x^2 + (1/2)x + (1/16)?
- 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 [11/24/1997]
Factor the expression by grouping: xy + ay - bx - ab .
- 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 Cubic Expressions [08/24/2010]
A student wonders how to factor polynomials of odd degrees. Doctor Ian suggests
exponent expansion and prime factorization.
- Factoring Equations with Many Variables [12/12/1996]
XY ( X - Y ) + 3Y (X - Y)^2
- Factoring in General [12/22/1995]
I have never figured out factoring. I can sort of do it but I don't
always get it right. Can you tell me how to factor better?
- Factoring into the Product of Two Trinomials [02/22/2003]
Write as a product of two trinomials with integer coefficients: 6x^2 -
xy + 23x - 2y^2 - 6y + 20
- Factoring Polynomials [11/29/1999]
How can I factor 4x^2 - 36, or x^2 + yz + xy + xz?
- Factoring Polynomials [3/14/1995]
I am having trouble factoring polynomials. I would appreciate it if you
could show me step-by-step instructions with examples.
- Factoring Polynomials [02/08/2003]
Factor: 9y^4 + 12y^2 + 4.
- Factoring Polynomials of Degree 2 [4/8/1996]
I am having a lot of difficulties factoring polynomials of the type:
x^2 + 6x +8 and 3x^2 + 10x +8.
- Factoring Polynomials of Degree 3 [3/17/1996]
Factor completely (x+2)^3 + (x+2)^2.
- Factoring Polynomials Using Substitution [09/26/2001]
I can't get two questions on my own: x^2+10xy+25y^2-81z^2 and a^4-6a^
- Factoring Polynomials with Common Expressions [08/20/2005]
A neat way to factor polynomial expressions like 8(x-3) - 2(x-3)² by
taking out a common factor using substitution.
- 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 Quadratic Trinomials [06/02/1998]
Is there a general process I can use to factor equations?
- Factoring to Simplify vs. Factoring to Solve [05/26/2014]
An adult wonders why the same factoring techniques that simplify rational expressions
do not also apply when solving rational equations. With worked examples, Doctor
Peterson troubleshoots the differences, then shares insights about multiplying by least
common denominators (LCD).
- Factoring Trinomials [04/13/2005]
Help on factoring d^2 - 33d - 280 and a general strategy for factoring
- Factoring Trinomials: 9x^2 - 42x + 49 [10/15/2002]
I am having a lot of trouble factoring this trinomial: 9x^2 - 42x +
- Factoring Trinomials by the Grouping Method [12/08/2005]
A discussion and proof of why factoring trinomials by grouping works.
- Factoring Trinomials in Quadratic Equations [02/15/2004]
A discussion of several methods of factoring that can be used to solve
the quadratic equation 15x^2 - 16x - 7 = 0.
- Factoring vs. Simplifying [03/02/2003]
Factor the expression 1+y(1+x)^2(1+xy).
- Factoring (x - 1)(x^2 - x - 2) [11/04/1997]
I don't remember how to factor.
- Factoring x^4 + (x^2)(y^2) + y^4 [04/25/2005]
Is there any mathematical way or pattern to factor the polynomial x^4
+ (x^2)(y^2) + y^4?
- Factorization [03/17/1999]
Can you help me simplify 9b^2 - 24bc + 16c^2?
- Find a Pair of Factors of AC Whose Sum is B [04/12/2002]
When I was a freshman, I was taught a method called A C Bust B, but I
can't remember it.
- Finding a Single Pair of Factors [02/27/2002]
Factor ax^2 - bx - c.
- Finding the Greatest Common Factor (GCF) [03/31/1998]
I need help finding the GCF of terms that include both numbers and
- Finding the Sum of Solutions of a Polynomial Equation [03/11/2004]
What is the sum of the solutions of x^3 + 2x^2 - 5x - 6 = 0 given that
x = 2 is a solution?
- Fractions and Lowest Terms [07/19/2001]
Simplifying expressions: how do you finish cancelling fractions, and then
what do you multiply? What is the lowest term?
- General Sign Patterns for Factoring Trinomials [04/12/2005]
How do the signs in the trinomial help tell you what signs will be in
each of the two binomials when it's factored?
- More Methodical Than Guessing [06/12/2017]
A young adult who prefers clear procedures struggles with guessing to calculate square roots and factor polynomials. Distinguishing between operations and algorithms, Doctor Peterson surveys a range of methods for finding roots and factoring — some of which require no guessing, others of which involve approximating — before emphasizing the intuition that develops with perseverance.
- Multiplying Algebraic Fractions [11/05/2002]
Factoring quadratic expressions to get binomials that cancel.
- No Difference of Squares [02/08/1997]
Factor 180x^2y - 108xy^2 -75x^3.
Search the Dr. Math Library:
© 1994- The Math Forum at NCTM. All rights reserved.
Home || The Math Library || Quick Reference || Search || Help