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- Polynomials Addition
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- Polynomials Multiplication
- Polynomials Division
- Check for Polynomial
- Degree of Polynomial
- Polynomial Equation Solver Calculator
- Leading Term of a Polynomial Calculator
- Ascending of a Polynomial
- Descending of a Polynomial
- Factoring Over Multivariable Polynomials
- GCF of Polynomials
- Factor Out GCF from Polynomials
- Determining if Polynomial is Prime
- Finding the LCM using GCF
- Factoring Binomials as Sum or Difference of cube
- Factoring Binomials as Difference of Squares
- Polynomial Root Calculator
- Expand using the Binomial Theorem
- Factoring over the Complex Numbers
- Remainder Theorem Calculator

**Ex:Add polynomials x⁴+3x²+5x⁴+10x³+x+5+12x³+7x²+8x**

The given expression is x⁴+3x²+5x⁴+10x³+x+5+12x³+7x²+8x

Group the similar terms x⁴+5x⁴+10x³+12x³+3x²+7x²+x+8x+5

Combine the similar terms 6x⁴+22x³+10x²+9x+5

Addition of x⁴+3x²+5x⁴+10x³+x+5+12x³+7x²+8x is 6x⁴+22x³+10x²+9x+5.

**Example: Subtract polynomials (6u²+5u²v²-3uv²)-(4u⁴+5u²v²-5uv).**

The given polynomial expression is (6u²+5u²v²-3uv²)-(4u⁴+5u²v²-5uv)

Remove all braces 6u²+5u²v²-3uv²-4u⁴-5u²v²+5uv

Group the similar terms -4u⁴+5u²v²-5u²v²+6u²-3uv²-5uv

After combining similar terms we get x^2 - x - 8 + 2

Combine the similar terms -4u⁴+6u²-3uv²-5uv

Subtraction of (6u²+5u²v²-3uv²)-(4u⁴+5u²v²-5uv) is -4u⁴+6u²-3uv²-5uv

**Example: Multiply polynomials (3x²+5x+10)(x²-3x-1)**

The given polynomial is (3x²+5x+10)(x²-3x-1)

Multiply each term of the first polynomial with every term of the second polynomial.

(3x²+5x+10)(x²-3x-1) = 3x²(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

= 3x²(x²)-3x²(3x)-1(3x²)+5x(x²)+5x(-3x)+5x(-1)+10(x²)-3x(10)+10(-1)

= 3x⁴+9x³-3x²+5x³-15x²-5x+10x²-30x-10

== 3x⁴+9x³+5x³-3x²-15x²+10x²-5x-30x-10

= 3x⁴+14x³-8x²-35x-10

Multiplication of (3x²+5x+10)(x²-3x-1) is 3x⁴+14x³-8x²-35x-10.

**Ex: Polynomial Division of (x^4+2x+8)/(x+6)**

The given expression is (x^4+2x+8)/(x+6)

The Divident is x^4 + 2 x + 8 and Divisor is x + 6

x + 6)x^4 + 2 x + 8(x^3 - 6 x^2 + 36 x - 214

- x^4 - 6 x^3

-----------------

- 6 x^3 + 2 x + 8

6 x^3 + 36 x^2

------------------

36 x^2 + 2 x + 8

- 36 x^2 - 216 x

------------------

8 - 214 x

214 x + 1284

------------

1292

After the division the quotient is x^3 - 6 x^2 + 36 x - 214 and reminder is 1292

**Ex: Determining x^5+3x^5+1+x^6+x^3+x Expression is a Polynomial**

The expression can be written as x^6 + 4 x^5 + x^3 + x + 1

polynomial is a combination of terms separated using + or − signs. Polynomials cannot contain any of the following:

i)Variables raised to a negative or fractional exponent.

i)Variables in the denominator.

iii)Variables under a radical.

iv)Special features. (trig functions, absolute values, logarithms, … ).

x^5+3x^5+1+x^6+x^3+x is a polynomial.

**Ex 1: Finding Polynomial x^5+x^5+1+x^5+x^3+x in Ascending Order**

The Given Polynomial is x^5+x^5+1+x^5+x^3+x

The ascending Order of polynimial is 1+x+x^3+3 x^5

**Ex 2: Find the Polynomial x^5+3x^5+1+x^6+x^3+x in Ascending Order**

The Given Polynomial is x^5+3x^5+1+x^6+x^3+x

The ascending Order of polynimial is 1+x+x^3+4 x^5+x^6

**Ex 3: Find the Polynomial x^3+x^5+1+x^3+x^3+x in Ascending Order**

The Given Polynomial is x^3+x^5+1+x^3+x^3+x

The ascending Order of polynimial is 1+x+3 x^3+x^5

**Ex 1: Determining Polynomial of Descending Order of x^5+x^5+1+x^5+x^3+x**

The Given Polynomial is x^5+x^5+1+x^5+x^3+x

The descending Order of polynimial is 3 x^5 + x^3 + x + 1

**Ex 2: Determining Polynomial of Descending Order of x^5+3x^5+1+x^6+x^3**

The Given Polynomial is x^5+3x^5+1+x^6+x^3

The descending Order of polynimial is x^6 + 4 x^5 + x^3 + 1

**Ex 3: Determining Polynomial of Descending Order of x^3+x^5+1+x^3+x^3+x**

The Given Polynomial is x^3+x^5+1+x^3+x^3+x

The descending Order of polynimial is x^5 + 3 x^3 + x + 1

**Ex 1: Degree of a Polynomial x^3+x^5+1+x^3+x^3+x**

The given expression is x^3+x^5+1+x^3+x^3+x

- The degree of x is 1
- The degree of x^3 is 3
- The degree of x^3 is 3
- The degree of x^5 is 5
- The degree of x^3 is 3
- The degree of 1 is 0

But the degree of expression will the highest degree of the indivisual expression of above i.e 5

**Ex 2: Degree of a Polynomial x^5+3x^5+1+x^6+x^3+x**

The given expression is x^5+3x^5+1+x^6+x^3+x

- The degree of x is 1
- The degree of x^3 is 3
- The degree of x^6 is 6
- The degree of x^5 is 5
- The degree of 3 x^5 is 5
- The degree of 1 is 0

But the degree of expression will the highest degree of the indivisual expression of above i.e 6

**Ex 1: Determining the Leading Term of a Polynomial x^5+3x^5+1+x^6+x^3+x**

The given input is x^5+3x^5+1+x^6+x^3+x

The term can be simplified as x^6 + 4 x^5 + x^3 + x + 1

-- 1 term has degree 0 .

-- x term has degree 1 .

-- x^3 term has degree 3 .

-- x^6 term has degree 6 .

-- 4 x^5 term has degree 5 .

--Here highest degree is maximum of all degrees of terms i.e 6 .

--Hence the leading term of the polynomial will be the terms having highest degree i.e x^6 .

--x^6 has coefficient 1 .

**Ex 2: Determining the Leading Term of a Polynomial xx^3+x^5+1+x^3+x^3+x**

The given input is x^3+x^5+1+x^3+x^3+x

The term can be simplified as x^5 + 3 x^3 + x + 1

-- 1 term has degree 0 .

-- x term has degree 1 .

-- x^5 term has degree 5 .

-- 3 x^3 term has degree 3 .

--Here highest degree is maximum of all degrees of terms i.e 5 .

--Hence the leading term of the polynomial will be the terms having highest degree i.e x^5 .

--x^5 has coefficient 1 .

**Ex 1: How to Find Factoring Multi Variable Polynomials for a^2-b^2?**

The given polynomial is a^2-b^2

The polynomial can be written as a^2 - b^2

=(a)(a)+(b)(a)+(a)(-b)+(b)(-b)

=(a)((a - b))+(b)((a - b))

=(a - b) (a + b)

**Ex 2: How to Find Factoring Multi Variable Polynomials for a^3-b^3?**

The given polynomial is a^3-b^3

The polynomial can be written as a^3 - b^3

=(a)(a^2)+(-b)(a^2)+(a)(ab)+(-b)(ab)+(a)(b^2)+(-b)(b^2)

=(a)((a2 + ab + b2))+(-b)((a2 + ab + b2))

=(a - b) (a^2 + a b + b^2)

**Ex 3: How to Find Factoring Multi Variable Polynomials for abc+8ab+ac+8a+bc+8b+c+8?**

The given polynomial is abc+8ab+ac+8a+bc+8b+c+8

The polynomial can be written as a b c + 8 a b + a c + 8 a + b c + 8 b + c + 8

=((ab)((c + 8))+(a)((c + 8))+(b)((c + 8))+(1)((c + 8)))

=((ab)((c + 8))+(a)((c + 8))+(b)((c + 8))+(1)((c + 8)))

=((a)(b)+(1)(b)+(a)(1)+(1)(1))(c + 8)

=((a)((b + 1))+(1)((b + 1)))(c + 8)

=(a + 1) (b + 1) (c + 8)

**Ex 1: Find the GCF of Polynomials x^2+2x+1,x+1**

The given input is x^2+2x+1,x+1

x^2+2x+1 has factors i.e (x + 1)^2

x+1 has factors i.e x + 1

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is x + 1 and simplified as x + 1

**Ex 2: Find the GCF of Polynomials x^2-1,x-1**

The given input is x^2-1,x-1

x^2-1 has factors i.e (x - 1) (x + 1)

x-1 has factors i.e x - 1

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is x - 1 and simplified as x - 1

**Ex 3: Find the GCF of Polynomials x^3-1,x+1**

The given input is x^3-1,x+1

x^3-1 has factors i.e (x - 1) (x^2 + x + 1)

x+1 has factors i.e x + 1

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is 1 and simplified as 1

**Ex 1: Find the Factor out GCF of Polynomials x^2+2x+1,x+1**

The given input is x^2+2x+1,x+1

x^2+2x+1 has factors i.e (x + 1)^2

x+1 has factors i.e x + 1

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is x + 1 and simplified as x + 1

Factor form of GCF is x + 1

**Ex 2: Find the Factor out GCF of Polynomials x^2-1,x-1**

The given input is x^2-1,x-1

x^2-1 has factors i.e (x - 1) (x + 1)

x-1 has factors i.e x - 1

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is x - 1 and simplified as x - 1

Factor form of GCF is x - 1

**Ex 3: Find the Factor out GCF of Polynomials x^3-1,x+1**

The given input is x^3-1,x+1

x^3-1 has factors i.e (x - 1) (x^2 + x + 1)

x+1 has factors i.e x + 1

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is 1 and simplified as 1

Factor form of GCF is 1

**Ex 1: Finding Is x^5+x^5+1+x^5+x^3+x Prime Polynomial**

The given polynomial is x^5 + x^5 + x^5 + x^3 + x + 1

So x^5 + x^5 + x^5 + x^3 + x + 1 = 3 x^5 + x^3 + x + 1

It is a prime polynomial because it has only two factors i.e 1 and 3 x^5 + x^3 + x + 1

**Ex 2: Finding Is x^5+3x^5+1+x^6+x^3+x Prime Polynomial**

The given polynomial is x^6 + x^5 + 3 x^5 + x^3 + x + 1

So x^6 + x^5 + 3 x^5 + x^3 + x + 1 = x^6 + 4 x^5 + x^3 + x + 1

It is a prime polynomial because it has only two factors i.e 1 and x^6 + 4 x^5 + x^3 + x + 1

**Ex 3: Finding Is x^3+x^5+1+x^3+x^3+x Prime Polynomial**

The given polynomial is x^5 + x^3 + x^3 + x^3 + x + 1

So x^5 + x^3 + x^3 + x^3 + x + 1 = x^5 + 3 x^3 + x + 1

It is a prime polynomial because it has only two factors i.e 1 and x^5 + 3 x^3 + x + 1

**Ex 1: Finding LCM of Polynomials x^2+2x+1, x+1 Using GCF**

The given Expressions are x^2+2x+1,x+1

x^2+2x+1 has factors i.e (x + 1)^2

x+1 has factors i.e x + 1

By finding the GCF of given expressions we get that the gcf is x + 1

There are 2 number of expressions are given.

To find the LCM we have to first multiply all the expressions (x^2+2x+1)(x+1) = x^3 + 3x^2 + 3x + 1

To find the LCM we have devide 2-1 power of gcf from x^3 + 3x^2 + 3x + 1

So by dividing x + 1 from x^3 + 3x^2 + 3x + 1 = (x^3 + 3x^2 + 3x + 1)/(x + 1) = x^2 + 2x + 1

So the LCM of x^2+2x+1,x+1 is x^2 + 2x + 1

**Ex 2: Finding LCM of Polynomials x^2-1, x-1 Using GCF**

The given Expressions are x^2-1,x-1

x^2-1 has factors i.e (x - 1)(x + 1)

x-1 has factors i.e x - 1

By finding the GCF of given expressions we get that the gcf is x - 1

There are 2 number of expressions are given.

To find the LCM we have to first multiply all the expressions (x^2-1)(x-1) = x^3 - x^2 - x + 1

To find the LCM we have devide 2-1 power of gcf from x^3 - x^2 - x + 1

So by dividing x - 1 from x^3 - x^2 - x + 1 = (x^3 - x^2 - x + 1)/(x - 1) = x^2 - 1

So the LCM of x^2-1,x-1 is x^2 - 1

**Ex 3: Finding LCM of Polynomials x^3-1, x+1 Using GCF**

The given Expressions are x^3-1,x+1

x^3-1 has factors i.e (x - 1)(x^2 + x + 1)

x+1 has factors i.e x + 1

By finding the GCF of given expressions we get that the gcf is 1

There are 2 number of expressions are given.

To find the LCM we have to first multiply all the expressions (x^3-1)(x+1) = x^4 + x^3 - x - 1

To find the LCM we have devide 2-1 power of gcf from x^4 + x^3 - x - 1

So by dividing 1 from x^4 + x^3 - x - 1 = (x^4 + x^3 - x - 1)/(1) = x^4 + x^3 - x - 1

So the LCM of x^3-1,x+1 is x^4 + x^3 - x - 1

**1. How to solve polynomial equations online?**

To solve polynomial equation problems, choose Polynomial Equation Solver Calculator and enter the polynomial expression. Tap on the calculate button to get the values of the variable in less time.

**2. What is the polynomial formula?**

The polynomial formula has variables with different powers, the highest power of the variable is called the degree of the polynomial. The general polynomial formula is given as ax^{n-1} + cx^{n-3} + .... + rx + s. Here, a, b, c .. are coefficients, n is the degree of the polynomial and x is the variable.

**3. How to use polynomials calculator?**

All you need to do is provide the polynomial details in the mentioned input sections of the respective Polynomial Calculator and press the calculate button. You will get the output in a fraction of seconds.

**4. How do you factor polynomials? **

To find factors of the polynomials easily, visit trusted website factorpolynomials.com and check for the online calculator to obtain the result quickly.