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order of operations
Browse High School Polynomials
Stars indicate particularly interesting answers or
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Selected answers to common questions:
Completing the square.
- Cubic Equations in One Formula [11/27/2001]
I know the formula for solving quadratic equations of the type
ax^2+bx+c=0, but is there a formula for cubic equations?
- Decomposing Fractions [04/08/2009]
Finding the sum of 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(29*30) by
decomposing into partial fractions.
- Defining Quadratic Formula [01/21/2002]
Taking successive differences in a sequence.
- Definition of a Polynomial [12/04/1997]
Is just x a polynomial?
- Definition of Monomial [04/26/2004]
Do monomials include quotients of variables? For example, would x/y
or xy^-2 be considered a monomial?
- Definitions of Monomials and Polynomials [03/11/2004]
Why is 1/x considered not to be a monomial? It could be written as
x^(-1) which is just one term. My math text says that it is NOT a
monomial but it does not say why.
- Degree of a Constant [12/02/2002]
Why is the degree of a constant zero?
- Degree of a Polynomial [12/31/1994]
If the degree of a monomial is the sum of the exponents of its variables, so that x^3*y^2 is degree 5, what happens in the case of x^3*y^(-2)? Is it degree 1 or would you apply absolute value and also call it degree 5?
- Degree of a Rational Function [06/19/2003]
Given: f(x) = p(x)/q(x). Prove that if the highest degree of p(x) is
smaller than the highest degree of q(x), the horizontal is y=0.
- Degree of Constant Function [11/08/2001]
We think F(x) = 1x^0 is not a polynomial function (because polynomials
shouldn't have discontinuities), but F(x) = 1 is a polynomial. And F(x) =
1 still has degree 0 but for reasons we can't explain.
- Degree of Zero [02/25/2003]
What is the degree of zero?
- Descartes - Rule of Signs [06/26/1998]
I'm trying to find the number of positive and negative real zeros for a
- Descartes' Rule of Signs and Complex Roots [08/04/1998]
Prove that if p and q are real and q is not equal to 0, the equation x^3
+ px +q = 0 has two imaginary roots.
- 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 Cubes [11/18/1996]
What two positive integers satisfy the condition that the difference of
their cubes is 56,765?
- 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?
- Difference Tables [05/09/1997]
Why is it that with almost any values for the difference table, a common
number is always reached to determine the degree of the equation?
- A Different Binomial Expansion Theorem [07/23/1998]
I'm looking for an alternate version of the famous binomial expansion
- 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)?
- Dividing Polynomials [03/06/1997]
The polynomial p(x) with integer coefficients satisfies (1) if p(x) is
divided by x^2-4x+3, the remainder is 65x-68, and (2) if p(x) is divided
by x^2+6x-7, the remainder is -5x+a. Find a.
- Dividing Polynomials [8/18/1996]
How do I simplify ([a^3-6a^2+8a]/5)/([2a-4]/[10a-40])?
- Dividing two Polynomials [6/28/1996]
Divide these two Polynomials: 12(x^2 - 4x + 3) / x^3 - 3x^2 -x
- Division of Unknown Polynomials [3/18/1996]
When a polynomial P(x) is divided by x-1, the remainder is 3. When P(x)
is divided by x-2, the remainder is 5. Find the remainder when P(x) is
divided by x^2-3x+2.
- Eisenstein's Irreducibility Criterion [02/26/2003]
Is Eisenstein's irreducibility criterion necessary or sufficient for a
polynomial to be irreducible?
- Equations and Factoring [2/5/1996]
Solve. Identify all double roots: 2(r^2 + 1)=5r
- Expanding Binomials and Pascal's Triangle [06/07/1998]
How does expanding a binomial relate to Pascal's Triangle?
- Expression vs. Equation [03/20/2003]
What is the difference between an expression and an equation?
- 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-
- 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 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?