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Factor expressions step by step
The calculator will try to factor any expression (polynomial, binomial, trinomial,
quadratic, rational, irrational, exponential, trigonometric, or a mix of them), with steps shown. To do this, some substitutions are first applied to convert the expression into a polynomial, and then the following techniques 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, and the rational zeros theorem.
Solution
Your input: factor $$$x^{4} - 20 x^{2} + 64$$$.
We can treat $$$x^{4} - 20 x^{2} + 64$$$ as a quadratic function with respect to $$$x^{2}$$$.
Let $$$Y = x^{2}$$$.
Temporarily rewrite $$$x^{4} - 20 x^{2} + 64$$$ in terms of $$$Y$$$: $$$x^{4} - 20 x^{2} + 64$$$ becomes
$$$Y^{2} - 20 Y + 64$$$.
To factor the quadratic function $$$Y^{2} - 20 Y + 64$$$, we should solve the corresponding quadratic equation $$$Y^{2} - 20 Y + 64=0$$$.
Indeed, if $$$Y_1$$$ and $$$Y_2$$$ are the roots of the quadratic equation $$$aY^2+bY+c=0$$$, then $$$aY^2+bY+c=a(Y-Y_1)(Y-Y_2)$$$.
Solve
the quadratic equation $$$Y^{2} - 20 Y + 64=0$$$.
The roots are $$$Y_{1} = 16$$$, $$$Y_{2} = 4$$$ (use the quadratic equation calculator to see the steps).
Therefore, $$$Y^{2} - 20 Y + 64 = \left(Y - 16\right) \left(Y -
4\right)$$$.
Recall that $$$Y = x^{2}$$$: $$$x^{4} - 20 x^{2} + 64 = 1 \left(x^{2} - 16\right) \left(x^{2} - 4\right)$$$.
$$\color{red}{\left(x^{4} - 20 x^{2} + 64\right)} = \color{red}{1 \left(x^{2} - 16\right) \left(x^{2} - 4\right)}$$
Apply the difference of
squares formula $$$\alpha^{2} - \beta^{2} = \left(\alpha - \beta\right) \left(\alpha + \beta\right)$$$ with $$$\alpha = x$$$ and $$$\beta = 2$$$:
$$\left(x^{2} - 16\right) \color{red}{\left(x^{2} - 4\right)} = \left(x^{2} - 16\right) \color{red}{\left(x - 2\right) \left(x + 2\right)}$$
Apply the
difference of squares formula $$$\alpha^{2} - \beta^{2} = \left(\alpha - \beta\right) \left(\alpha + \beta\right)$$$ with $$$\alpha = x$$$ and $$$\beta = 4$$$:
$$\left(x - 2\right) \left(x + 2\right) \color{red}{\left(x^{2} - 16\right)} = \left(x - 2\right) \left(x + 2\right)
\color{red}{\left(x - 4\right) \left(x + 4\right)}$$
Thus, $$$x^{4} - 20 x^{2} + 64=\left(x - 4\right) \left(x - 2\right) \left(x + 2\right) \left(x + 4\right)$$$.
Answer: $$$x^{4} - 20 x^{2} + 64=\left(x - 4\right) \left(x - 2\right) \left(x + 2\right) \left(x + 4\right)$$$.
quadratic factoring calculator
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AuthorMessage
long Registered: 04.01.2002 From:
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Posted: Thursday 28th of Dec 07:00
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| Will somebody be able to solve my problem with my math? I have attempted to find myself a coach who can help me . But till now I have failed. Its difficult to locate someone reachable and affordable . But then I want to find a solution to my problem with quadratic factoring calculator as my exams are coming up just now. It will be a immense help for me if somebody can assist me.
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kfir Registered: 07.05.2006 From: egypt
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Posted: Friday 29th of Dec 08:15
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| Can you be a bit more clear about quadratic factoring calculator ? I conceivably able to help you if I knew few more details . A good quality software provide solution to your problem instead of paying for a algebra tutor. I have tried many math program and guarantee that Algebrator is the best program that I have stumbled onto . This Algebrator will solve any math problem that you enter and it also explains every step of the – you can exactly write it down
as your homework assignment. However, this Algebrator should also help you to learn algebra rather than only use it to copy answers.
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Jrahan
Registered: 19.03.2002 From: UK
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Posted: Saturday 30th of Dec 09:37
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| I didn’t use that Algebrator software yet but I heard from my peers that it really does assist in answering algebra problems. Since then, I noticed that my peers don’t really have troubles solving some of the problems in class. It might really have been effective in improving their solving skills in algebra. I am eager to use it someday because I think it can be very useful and help me have a good mark in algebra.
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alhatec16 Registered: 10.03.2002 From: Notts, UK.
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Posted: Sunday 31st of Dec 08:45
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| multiplying matrices, function definition and function domain were a nightmare for me until I found Algebrator, which is really the best math program that I have ever come across. I have used it through many algebra classes – College Algebra, College Algebra and Algebra 2. Simply typing in the algebra problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I really recommend the
program.
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enon Registered: 22.06.2005 From:
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Posted: Monday 01st of Jan 09:44
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| I can’t believe it. You really mean it? Is it as straight forward as that? Wonderful . I am greatly relieved to hear this. Do tell me where can I get this program?
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ZaleviL Registered: 14.07.2002 From: floating in the light, never forgotten
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Posted: Wednesday 03rd of Jan 10:24
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| Accessing the program is simple . All you want to know about it is available at //polymathlove.com/simple-trinomials-as-products-of-binomials.html. You are guaranteed satisfaction. And in addition , there is a money-back guarantee. Hope this is the end of your search .
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What are the steps in solving quadratic equation by factoring?
Steps for Solving Quadratic Equations by Factoring.
Write the equation in standard form:.
Factor completely..
Apply the Zero Product Rule , by setting each factor containing a variable to zero. If ab = 0, then a = 0 or b = 0..
Solve the linear equations in step 3..
Check..
What are the 4 steps to solve a quadratic equation?
The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. So what I want to talk about now is an overview of all the different ways of solving a quadratic equation.
What are the 5 steps in solving worded problems involving quadratic equation?
Steps for solving Quadratic application problems:.
Draw and label a picture if necessary..
Define all of the variables..
Determine if there is a special formula needed. ... .
Write the equation in standard form..
Factor..
Set each factor equal to 0. ... .
Check your answers..