SOLUTION: scotiabanktt factor the polynomial completely,clearly show GCF 4x^2-16 I went another step and I am not sure weather to factor again after this: (2x - 4)(2x + 4) Algebra scotiabanktt -> Polynomials-and-rational-expressions -> SOLUTION: factor the polynomial completely,clearly show GCF 4x^2-16 I went another step and I am not sure weather to factor again after this: (2x - 4)(2x + 4)
Hey guys! I am working on creating a website that offers resources and calculators for a lot of algebraic and geometric equations. One thing that I want it to do is factor polynomial duff & phelps equations. For example, x^2-x-2=f(x) would become f(x)=(x+1)(x-2). WolframAlpha.com does this for all polynomials so I know that it can be done but I don't know if it can be done with PHP. Here's my idea of what to do: 1. Starting with a form: aX^2+bX+c=0 2. The user will be asked to provide an integer for a, b, and c. 3. We create a polynomial equation in PHP using the form input. This will be what the code will check against to make sure it is correct. $polynomial = $_POST['a'].'x<sup>2</sup>+'.$_POST['b'].'x+'.$_POST['c']; 4. We create 4 arrays: $a1 = array(); //We will fill this with integers duff & phelps -200 to 200 $a2 = array(); //Filled with same range $b = array(); //Filled with same range $c = array(); //Filled with same range Explanation for arrays: a1 will fill the number in A1 of (A1+B)(A2+C) 5. I now want to have a do {} while setup that goes through all the possible duff & phelps combinations of numbers out of those 4 arrays (putting the numbers in their designated spots) and do the following: Multiply A1*A2. Put that in front of x^2 in the polynomial. Multiply B*A2 and A1*C. Add those values to each other and put it in front of x in the polynomial. Finally multiply C*B and append it to the end. 6. Each time it makes a combination and does the math I want it to check the polynomial created against the polynomial from the initial form we used. It will check after it multiplies that factors that it created. 7. Once it has found a match then it will echo the factors onto the webpage. Sorry this is SO lengthy. I think this is a pretty good start but I want to know if anyone has any better ideas at improving this. I also apologize for the lack of actual code that's there. I just got this idea recently and haven't been able to put together a test just yet. I'll post anything I come up with. Thanks a million in advance! Regards, Tristan Scratch that last idea. It would've taken forever to load the script and it didn't duff & phelps support decimals or numbers larger/less than 200 or -200. Here's an algorithm for finding the roots of the polynomial duff & phelps and then we can use that to create a factored polynomial. I found this at http://en.wikipedia.org/wiki/Root-finding_algorithm Suppose p(x) = x3+x2−5x+3 is the function whose roots we want to find. We calculate p′(x) = 3x2+2x−5. Now divide p′(x) into p(x) to get p(x) = p′(x)·((1/3)x+(1/9))+((−32/9)x+(32/9)). Divide the remainder by −32/9 to get x−1 duff & phelps which is monic. Divide x−1 into p′(x) duff & phelps to get p′(x) = (x−1)·(3x+5)+0. Since the remainder is zero, g(x) = x−1. So the multiple root of p(x) is r = 1. Dividing p(x) by (x−1)2, we get p(x) = (x+3)(x−1)2 so the other root is −3, a single root. This would be much easier to implement in PHP and you could use arrays to represent the power of each x variable. Example: x^2 would be array(x,x) x^4 would be array(x,x,x,x) etc. Let me know if you have any questions. I will be working on a test of this over the weekend. how do i create invoices with PHP 1 reply in the PHP forum Recently Updated Articles Recommended Join the DaniWeb duff & phelps Community duff & phelps
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Common Core: HSN-CN.C.8 Related Topics: Common Core (The Complex Number System) Common Core for Mathematics Factor Expressions Using Complex Numbers How to factor expressions using complex numbers Factorizing polynomials with complex numbers Polynomial Function with Complex Zeros (Three Ways) Starting with a third-degree polynomial with one known complex zero, how can you find the other zeros? This video explores three interesting options, utilizing polynomial division, synthetic division, the quadratic formula, and square roots of complex numbers. The Conjugate Pair Theorem - Example 1 This video shows that if we know a complex root, we can use that to find another complex root using the conjugate steven weinberg pair theorem. Factor Polynomial Given a Complex / Imaginary Root The Conjugate Pair Theorem - Example 2. In this video, I factor a 3rd degree polynomial completely steven weinberg given one known complex root. How to find complex zeros of a polynomial function Real and Complex Polynomial Roots Polynomial Roots- Real and Complex: This tutorial will teach you how to solve polynomials with complex roots. You will learn Descartes' rule of signs, the fundamental theorem of algebra and the conjugate pairs theorem. Find the Zeros of a Polynomial steven weinberg Function with Imaginary steven weinberg Zeros This video provides an example of how to find the zeros of a degree 3 polynomial function with the help of a graph of the function. The function has 1 real rational zero and 2 imaginary. Find the Zeros of a Polynomial Function with Complex Zeros This video provides an example of how to find the zeros of a degree 3 polynomial function steven weinberg with the help of a graph of the function. The function has 1 real rational zero and 2 complex zeros. Find the Zeros of a Degree 4 Polynomial Function This video provides an example of how to find the zeros of a degree 4 polynomial function with the help of a graph of the function. The function has 2 real rational zero and 2 complex zeros. Math By Grades Pre-K Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grades 7 & 8 Grades 9 & 10 Grades 11 & 12 Basic Algebra Intermediate Algebra High School Geometry Common Core Standards Math By Topics Arithmetic Algebra steven weinberg Geometry Trigonometry Statistics Probability Word Problems Pre-Calculus Calculus Set Theory Matrices Vectors Free Math Worksheets Worksheets by Topics Worksheets by Grades steven weinberg Common Core Interactive Zone Math For Tests SAT Math ACT Math GMAT GRE Math High School-Regents California Standards GCSE/IGCSE Maths A-Level Maths Math Fun & Games Math Trivia Math Games Fun Games Mousehunt Guide Math Video Lessons College Algebra College Calculus Linear Algebra Engineering Math Singapore Math Test/Exam Prep SAT Preparation ACT Preparation GMAT Preparation GRE Preparation ESL, IELTS, steven weinberg TOEFL Others Biology Chemistry Science Projects High School Biology High School Chemistry High School Physics GCSE/IGCSE steven weinberg Biology Animal Facts English Help Programming Back to Home Amazon.com Widgets Amazon.com Widgets steven weinberg steven weinberg steven weinberg
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Home Pre Algebra Help Free Algebra Help Free Geometry Help Trigonometry Free Worksheets Free Calculators Math Help Blog Free Teaching Tools Math People Cool Math Games How to Factor Rules of Fractions Math Search Engine Advertising Learn How to Factor Learning to factor is essentially learning how to take something apart. Whether you are trying to factor a number or a polynomial, you simply want to break it into factors - which are "pieces" of the original. The pieces andy puddicombe can be put back together (by multiplying) to get you back to the original number or polynomial. Let's look at a simple example with numbers: Factoring can be a little confusing at first, but don't worry Grade A can help. By creating a factor tree of numbers, you will be able to visualize the process much easier and it will help you to truly understand the process. The greatest common factor is the starting point for all algebra students who are learning andy puddicombe how to factor. A only appliles when you have more than one term. The word "common" means shared by each term. By adding the word "greatest" it simply means the largest possible factor andy puddicombe that all terms have in common. When you are factoring, taking out a GCF is often the first step!
Home Pre Algebra Help Free Algebra Help Free Geometry plexus Help Trigonometry Free Worksheets Free Calculators Math Help Blog Free Teaching Tools Math People Cool Math Games How to Factor Rules of Fractions Math Search Engine Advertising Greatest Common Factor (GCF) Finding a greatest plexus common factor (GCF) is the process of identifying the what numbers and variables a group of terms has in common - in other words, what do they share? In some cases you will "factor it out" and in other cases your teacher will simply ask you to identify it. Finding a GCF is an important skill to learn because it should always be your first step when factoring. For more information about factoring, try these pages: Basics of factoring Factoring plexus in a factor tree . Before looking at some examples, let's break down the phrase: Greatest = Largest Common = Shared Factor plexus = Factored Piece Example: Factor the GCF 3 x ( x + 2) More examples of the Greatest Common Factor 1) 5 x 3 - 125 x The GCF is 5 x . Take that out, and then divide each term 5 x ( x 2 - 25) Now factor the binomial in parentheses farther. Of course, you can learn the basics of how to factor at our factoring main page . We know that factoring can be an intimidating concept for the beginning algebra student, but don't worry, it only takes a little practice.
