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Polynomial factoring calculator
Polynomial factoring calculator converts polynomials to factored form. The calculator can be used to factor polynomials having one or more variables. Calculator shows all the work and provides detailed explanation how to factor the expression.
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Polynomial Factoring Techniques
To find the factored form of a polynomial, this calculator employs the following methods:
1 . Factoring GCF, 2 Factoring by grouping, 3 Using the difference of squares, and 4 Factoring quadratic polynomials.
Method 1 : Factoring GCF
Example 01: Factor 3ab 3 -6a 2 b
Method 2 : Factoring By Grouping
The method is very useful for finding the factored form of the four term polynomials.
Example 03: Factor 2a-4b+a 2 -2ab
We usually group the first two, and the last two terms.
We now factor 2 out of the blue terms and a out of from red ones.
At the end we factor out common factor of (a-2b)
Example 04: Factor 5ab+2b+5ac+2c
This is a rare situation where the first two terms of a polynomial do not have a common factor, so we have to group the first and third terms together.
Method 3 : Special Form – A
The most common special case is the difference of two squares.
a 2 -b 2 =(a+b)(a-b)
We usually use this method when the polynomial has only two terms.
Example 05: Factor 4x 2 -y 2 .
First, we need to notice that the polynomial can be written as the difference of two perfect squares.
4x 2 -y 2 =(2x) 2 -y 2
Now we can apply above formula with a=2x and b=y
(2x) 2 -y 2 =(2x-y)(2x+y)
Example 06: Factor 9a 2 b 4 -4c 2
The binomial we have here is the difference of two perfect squares, thus the calculation will be similar to the last one.
Method 4 : Special Form – B
The second special case of factoring is the Perfect Square Trinomial
a 2 ± 2ab + b 2 = (a ± b) 2
Example 07: Factor 100+20x+x 2
In this case, the first and third terms are perfect squares. So we can use the above formula.
Method 5: Factoring Quadratic Polynomials
The best way to explain this method is by using an example.
Example 08: Factor x 2 + 3x + 4
We know that the factored form has the following pattern
All we have to do now is fill in the blanks with the two numbers. To do this, notice that the product of these two numbers has to be 4 and their sum has to be 5. We conclude, after some trial and error, that the missing numbers are 1 and 4 . As a result, the solution is::
Example 09: Factor x 2 - 8x + 15
Like in the previous example, we look again for the solution in the form
The sum of missing numbers is -8 so we need to find two negative numbers such that the product is 15 and the sum is -8 . It is not hard to see that two numbers with such properties are -3 and -5 , so the solution is.
1. Polynomial factoring tutorial — factoring out greatest common factor, factoring by grouping, quadratics and polynomials with degree greater than 2.
2. Youtube tutorial demonstrates some of the most important polynomial factoring techniques.
3. 70 Fully Solved Factoring Problems
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Factoring Polynomials Calculator
Factor polynomials step by step.
The calculator will try to factor any polynomial (binomial, trinomial, quadratic, etc.), with steps shown. The following methods are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, the rational zeros theorem. The calculator accepts both univariate and multivariate polynomials.
Enter a polynomial:
If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.
Handling polynomials is made easier with our Factoring Polynomials Calculator. Whether you're tackling a challenging polynomial or merely refining your algebra knowledge, this tool is designed to ease the task.
How to Use Our Factoring Polynomials Calculator?
Begin by entering your polynomial into the designated field. Ensure that the coefficients and terms are correctly inputted.
Calculation
After inputting the polynomial, click the "Calculate" button.
The calculator will display the factored form of the polynomial. If the polynomial can't be factored, the calculator will notify you.
What Is Factoring?
Factoring, in mathematics, refers to decomposing a mathematical expression or number into a product of other numbers or expressions. When you factor an expression, you find two or more quantities that, when multiplied together, give the original expression.
For instance, consider the number $$$ 10 $$$ . It can be factored as $$$ 2\cdot5 $$$ . Here, $$$ 2 $$$ and $$$ 5 $$$ are the factors of $$$ 10 $$$ .
Why Is Factoring Important?
Understanding the factors of a polynomial is crucial in solving polynomial equations. It's akin to breaking down a problem into smaller, more manageable pieces. With a grasp of the essential factoring methods and techniques, you can solve a wide range of mathematical problems more effectively.
What Is Factoring Polynomials?
Factoring polynomials is a process in algebra where a polynomial is expressed as the product of two or more polynomial factors. It's akin to breaking down a number into its prime factors. By factoring, we are looking for polynomial expressions that, when multiplied together, will produce the original polynomial.
For example, the polynomial $$$ x^2-9 $$$ can be factored as $$$ (x+3)(x-3) $$$ . Another example is $$$ x^2+5x+6 $$$ , whose factors are $$$ x + 2 $$$ and $$$ x + 3 $$$ .
Factoring polynomials is a foundational technique in algebra, serving various purposes:
- Simplifying complex expressions.
- Solving polynomial equations.
- Graphing polynomial functions, since the zeros (roots) of the polynomial can be easily identified once the polynomial is factored.
Different methods are used to factor polynomials depending on their form and degree, including:
- Factoring out the greatest common factor (GCF).
- Using unique factorization formulas like the difference of squares or cubes.
- Quadratic trinomials factoring, and more.
The ability to factor polynomials can greatly assist in understanding and solving more complex mathematical problems.
Why Choose Our Factoring Polynomials Calculator?
Accuracy assured.
Our calculator processes even the most complex polynomials, ensuring accurate factorization every time.
User-Friendly Design
With an intuitive interface, even those new to the world of algebra will find it simple to use.
Step-by-Step Solutions
Beyond just answering, our tool provides detailed solutions, breaking down the factoring process for enhanced understanding.
Versatility
Whether you're tackling quadratic trinomials, cubic equations, or higher-degree polynomials, our calculator is up to the task.
How do I input my polynomial?
Simply enter your polynomial in the provided input field, ensuring you include all coefficients and variables. Then, click on the "Calculate" button.
What is the Factoring Polynomials Calculator used for?
The Factoring Polynomials Calculator is designed to help users break down a polynomial into its simplest factors. This assists in understanding and solving polynomial equations more efficiently.
I'm new to polynomials. Do you provide any explanations or steps?
Yes, our calculator offers a step-by-step breakdown of the factoring process, making it easier for learners to understand the methodology behind the results.
How is factoring polynomials helpful in real-life situations?
Factoring polynomials is a fundamental skill in algebra. It's crucial for solving polynomial equations, which have applications in engineering, physics, and economics.
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Polynomial Factorization Calculator
Get detailed solutions to your math problems with our polynomial factorization step-by-step calculator . practice your math skills and learn step by step with our math solver. check out all of our online calculators here ., example, solved problems, difficult problems.
Here, we show you a step-by-step solved example of polynomial factorization. This solution was automatically generated by our smart calculator:
Factor the polynomial $14a-21b+35$ by it's greatest common factor (GCF): $7$
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