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 TOPICS This page:   polynomials    Search   Dr. Math See also the Dr. Math FAQ:   cubic and   quartic equations and   order of operations Internet Library:   polynomials HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry 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. 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? 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. 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. Page: []

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