Form a polynomial with real coefficients calculator

Summary :

The degree function calculates online the degree of a polynomial.

degree online

Description :

The computer is able to calculate online the degree of a polynomial.

Calculating the degree of a polynomial

The calculator may be used to determine the degree of a polynomial.

To obtain the degree of a polynomial defined by the following expression `x^3+x^2+1`, enter : degree(`x^3+x^2+1`) after calculation, the result 3 is returned.

Calculating the degree of a polynomial with symbolic coefficients

The calculator is also able to calculate the degree of a polynomial that uses letters as coefficients.

To obtain the degree of a polynomial defined by the following expression : `ax^2+bx+c` enter degree(`ax^2+bx+c`) after calculation, result 2 is returned.

Syntax :

degree(polynomial)

Examples :

degree(`x^3+x^2+1`), returns 3

Calculate online with degree (degree of a polynomial)

Press J to jump to the feed. Press question mark to learn the rest of the keyboard shortcuts

Found the internet!

r/askmath

Posted by1 year ago

Archived

I have found a million calculators and methods for Mathway & Wolfram Alpha for turning a function into degrees / coefficients, but not the other way around. Help?

"Question Use the given information about the polynomial graph to write the polynomial. Write the polynomial in standard form axn+bxn−1+….

Degree: 3, Zeros at (8,0), (−4,0), (1,0), y-intercept (0,32). Leading coefficient is 1."

This thread is archived

New comments cannot be posted and votes cannot be cast

level 1

No, you don't need a calculator. You need to understand the math.

If f(x)=k(x-a)(x-b)(x-c)

=> f(a)=0, f(b)=0, f(c)=0

The question gives you a,b,c,k directly. You just need to expand it using the distributive law.

level 2

Knewton counted my answer as wrong though and with it, it's never clear until you fail out of the question if it's formatting or content. f(x)=x3 -5x2 -28x +32

level 1

y=a(x-8)(x+4)(x-1).

Plug in (0, 32) and solve for a

level 2

I got 1 for a but Knewton doesn't like me

This standard form calculator is basically a tool that finds multiple things about polynomials, the main of them being the Standard form of a polynomial equation.

After Hitting the calculate button, the user first sees the polynomial in standard form. Then there is 

• Factorization over complexes or splitting fields.
• Plot 
• Factorization over finite fields.

You can see the steps for each calculation. 

How to use polynomial standard form calculator?

To write polynomials in standard form using this calculator;

1. Enter the equation. Or you can load an example.
2. Double-check your equation in the displayed area.
3. Click Calculate.
4. Reset to use again.

What is the polynomial standard form?

Each equation type has its standard form. Radical equation? Check. Rational equation? Check. This means there is also a standard form of polynomial or exponential equations.

The standard form of the polynomial equation is obtained by ordering elements in the descending order of degrees. Its general form is 

Let’s see some examples of these equations.

Example 1:

Order the following equation in standard form. 

7x - 3 + 5x2

Solution:

Step 1: See the order of the polynomial.

The highest degree tells the order of the polynomial equation. In this example, the order of the polynomial is 2.

Step 2: Write the element with degree 2 in the first place.

5x2 is the required element.

5x2 + (second value) + (third value)

Step 3: Place the degree 1 value.

7x has the power one.

5x2 + 7x + (third value)

Step 4: Input the last value with the variable degree 0.

5x2 + 7x - 3.

This is the standard form of the given equation.

Example 2:

Arrange the following equations in the standard form

1. x5 - 4x + 2x10
2. 1 + 8x3 + x + x2
3. 7 + 7x + 7x2 + 6x3 + 6x4 + 6x5

Solution:

1. 2x10 + x5 - 4x
2. 8x3 + x2 + x + 1
3. 6x5 + 6x4 + 6x3 + 7x2 + 7x + 7

Factorization of polynomial equation

Factorization, as you might know, is the process of breaking down a value into smaller values which on multiplication give the original equation or function. Quadratic equations can be broken down by quadratic formula and completing squares.

But a general method is to arrange the equation into standard form and simplify it. It is best explainable by an example. 

Consider that you have the equation  9x + 6x2y + 3xy. Let’s find its factors.

Firstly, arrange this equation into standard form.

= 6x2y + 3xy + 9x

See what you can extract from this equation. This value will be the GCF of all three entries of the equation. 

= 3x (2xy + y + 3)

So, 3x is the GCF of the equation 6x2y + 3xy + 9x. Now, this equation is at its simplest. It cannot be solved further.

Hence, the factors of this equation are 3x and 2xy + y + 3.

Polynomial graph plot

When a polynomial equation is plotted on a graph, the x-intercepts give the factors of the equation. For example

This is the graph of the polynomial equation x2 + 2x + 1. You can determine its factors by looking at the x-intercept.

The factors of this equations are x = -1 and x = -1.

Factorization over a finite field

The calculator above finds the factors of the equation in the Galois field 2. GF(2) is the smallest finite field that exists with the elements 0 and 1. 

Its resemblance to the binary system and boolean algebra makes it really useful in computer science and related fields.

How to find the factored form of a polynomial?

What is an example of a polynomial coefficient?

How to generate a polynomial using a calculator?

What is coefficient calculator?

How do you write a polynomial with roots?

How do you write a polynomial form?

How do you find a polynomial coefficient?