You will learn how to factor and solve Quadratic Equations in Standard Form when the leading coefficient A=1 and also when A ≠ 1. Our Step by Step Calculator allows you to factor and solve your own quadratic equation. Quick Example when A ≠ 1 A Quadratic Function in Standard Form : In Factored Form it looks like this: When distributing we get: Matching the Coefficients on both sides shows that the 2 Zeros r and s have to fulfill the 2 conditions: In Words: What if the leading coefficient A is not 1 ? Let’s factor Ax²+Bx+C=0 with A ≠ 1 . Setting b=B/A and c=C/A we
rewrite as The Factored Form looks like this: Distributing terms we get We again Match the Coefficients: It shows that the 2 Zeros r and s have to fulfill these 2 conditions: In Words: Sample Problem: How to Factor a Quadratic Equation?1) Factor Quadratic Equations with Leading coefficient A = 1 Additionally, they have to add to -6 which implies Therefore, the factored version is: When asked to solve the Quadratic Equation we use the above factored version and set each factor equal to 0: Thus, the 2 zeros are x=4 , x=2 Easy, wasn’t it? Tip: When using the above Factor Quadratic Equation Solver to factor 2) Factor Quadratic Equations when A ≠ 1 Since we multiply by A=2 to get as the factored form. Tip: When using the above Factor Quadratic Equation Solver to factor This Video gives a great explanation on how to factor quadratic equations when the leading coefficient is not 1:
Factor, expand or simplify polynomials with Wolfram|AlphaMore than just an online factoring calculatorWolfram|Alpha is a great tool for factoring, expanding or simplifying polynomials. It also multiplies, divides and finds the greatest common divisors of pairs of polynomials; determines values of polynomial roots; plots polynomials; finds partial fraction decompositions; and more. Learn more about:
Tips for entering queriesEnter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask about factoring.
Access instant learning toolsGet immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator Learn more about:
VIEW ALL CALCULATORS
What is factoring?A polynomial with rational coefficients can sometimes be written as a product of lower-degree polynomials that also have rational coefficients. In such cases, the polynomial is said to "factor over the rationals." Factoring is a useful way to find rational roots (which correspond to linear factors) and simple roots involving square roots of integers (which correspond to quadratic factors). Polynomials with rational coefficients always have as many roots, in the complex plane, as their degree; however, these roots are often not rational numbers. In such cases, the polynomial will not factor into linear polynomials. Rational functions are quotients of polynomials. Like polynomials, rational functions play a very important role in mathematics and the sciences. Just as with rational numbers, rational functions are usually expressed in "lowest terms." For a given numerator and denominator pair, this involves finding their greatest common divisor polynomial and removing it from both the numerator and denominator. Can Photomath do factoring?Just because math is getting more complicated doesn't mean we can't make it a little easier for ourselves! Factoring is one way we can make our calculations a little clearer and easier to follow.
|