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Dr. Math FAQ:
order of operations
Browse High School Polynomials
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Completing the square.
- Factoring a Degree 2 Polynomial [3/21/1996]
Questions like x^2 - 12x - 85 I don't get these factor things!
- 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 a Multivariate Polynomial: Strategies Beyond Grouping [11/11/2008]
Several doctors respond to the challenge of factoring the polynomial
x^3 + y^3 + z^3 - 3xyz by hand, each contributing insights into how
properties such as symmetry and homogeneity help with factorization
- Factoring and the Factor Theorem [09/28/1998]
I need help factoring x^3 - x^2 + x - 2 = 4.
- Factoring an Expression [8/5/1996]
How can I factor x^10+x+1?
- Factoring another Equation [11/14/1995]
40y squared + yz - 6z squared?
- 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 Cubic Polynomials [01/01/2002]
I have a lot of trouble factoring cubic polynomials like 10^3-3x^2-x=
f(x). What does it mean to factor a polynomial into "linear factors"?
- Factoring Expressions [01/19/1997]
Factor 3x-21, 5x^2y-15xy^2, 18x^2-27x, and 2a-8b-10.
- Factoring Polynomials [11/07/2001]
Factoring polynomials like 12x^3y^9 + 20x^5y^4.
- Factoring Polynomials [11/29/1999]
How can I factor 4x^2 - 36, or x^2 + yz + xy + xz?
- 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 [03/05/1998]
Factoring quadratics that occur in fractions.
- 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 Quartics [9/4/1996]
Can you help me factorize f(x) = x^4 - 6x^3 + 11x^2 - 6x + 1 and solve
f(x) = 0?
- Factoring Trinomials [02/24/2002]
My teacher gave me a method for factoring trinomials (ax^2 +bx +c). It's
not FOIL or the grouping method, though the first part is similar. What's
the logic/reason behind this method?
- 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 - Difference of Two Squares [12/22/1997]
How do I factor a perfectly square trinomial and a quadratic trinomial?
- 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 Trinomials With Prime Factors [05/16/2002]
Factor each trinomial using integers, if possible.
- 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?
- Finding a Single Pair of Factors [02/27/2002]
Factor ax^2 - bx - c.
- 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 Polynomials [04/29/1997]
Given a set of points, find the polynomial that fits them.
- Finding Roots of Polynomials with Complex Numbers [09/27/2001]
I read in the archives that you can find the roots of 3rd or higher-
degree polynomials with complex numbers...
- Finding Terms in a Binomial Expansion [03/27/2001]
How can I find the fifth term of (-5m+4n^3)^54?
- Finding the Roots of a Function [11/4/1996]
How do you find the positive roots of x^9+3x^8-5x^3+4x+6=0? Show that
x^n- 1=0 has exactly 2 roots if n is even, and only 1 real root if n is
- 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?
- Finding Zeros of Polynomials [11/13/2001]
Can you explain how to find the zeros of polynomials and give me an
example of an application?
- Find the Edge Lengths of a Cuboid [05/13/2003]
I am trying to discover the lengths of the edges of a cuboid when only
the diagonal, area, and volume are known.
- Find Values of x... [9/4/1996]
Determine all values of x for which (x^2-5x+5)^(x^2-2x-48)=1.
- The FOIL Method and Multiplying Polynomials [05/25/2008]
How do I multiply (d - 4)(d + 3) using the FOIL method?
- Formula for Finding Roots [1/20/1995]
I need to know the formula for finding the roots of any quadratic, cubic,
or quartic polynomial.
- Functional Similarities: Division by (x -c), and Evaluation at x = c [06/06/2016]
An adult notices similarities when evaluating a function and synthetically dividing it. Doctor Peterson clarifies the relationship between the two methods, introducing the Remainder Theorem along the way — then extends the insight.