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High School Archive

Browse High School Polynomials
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Completing the square.
    Quadratic equations.

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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 polynomial...

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 theorem.

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 >+ 3.

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- 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 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 methods generally.

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?

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