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High School Archive

Browse High School Polynomials
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Selected answers to common questions:
    Completing the square.
    Quadratic equations.

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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^ 2b^2-27b^4.

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 trinomials.

Factoring Trinomials: 9x^2 - 42x + 49 [10/15/2002]

I am having a lot of trouble factoring this trinomial: 9x^2 - 42x + 49.

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 odd

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.

Gaussian Elimination [01/11/2000]

How can you solve a system of linear equations using Gaussian elimination?

General Expression for Partial Fractions [02/09/1999]

Is there a general expression for converting a polynomial fraction into partial fraction form?

Graphing an Equation [11/08/1997]

Please explain how to graph this equation: y = a + b(x) + c(x^2) + ...

Graphing Multivariable Polynomials [02/20/2005]

I have a few questions about multivariable polynomials. Say we have the polynomial x + y + z, can this be graphed? I also really don't know anything about the z axis or how to graph on it.

Graphing Polynomial Functions in Factored Form [07/07/2004]

When graphing polynomial functions, why do factors of even multiplicity cause the graph to not cross the x-axis, while factors of odd multiplicity cause it to cross?

Graphing Quadratic Polynomials [02/07/2001]

Can you give me a simple explanation of how to graph quadratic polynomials like y = x^2 - 8x + 15?

How Are Functions and Expressions Related? [07/09/2004]

What is the relationship between a function and an expression? I don't see any relationship, they are two completely different things.

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