A Polynomial Equation Solver Calculator displays all the solutions for your equation in less time. Simply put your equation in the specified field and press the calculate button to find the resultant values within no time. Along with the quick exact solution, you can also get the manual procedure using our calculator.

**Polynomial Equation Solver Calculator: **Trying to find possible values of a variable in a polynomial equation and don’t know the proper calculations in an easier manner. Then, we are here to help you out in getting the solution for the polynomial equation. This online free calculator tool assists you understand the process to get the result by factoring or solving a polynomial using Synthetic Division method. Check out the below sections to solve your equation.

You can select either factorization or synthetic division method to solve polynomial equations. The simple steps to solve your equation using factoring is mentioned here. You must follow these steps while solving polynomial equations.

- Take any polynomial equation.
- Bring all the variable values to one side and the other side should be zero.
- If the equation is in the form of ax
^{n}+ax^{n-1}+ax^{n-2}--ax=0, separate one x from the equation - Find the each value of x by finding the factors.

- Consider any polynomial equation
- Get all the variables of the equation to one side
- Find out the one number that satisfies your equation by checking the factors of constant
- Take all the coefficients of the equation
- Write the first number as it as and follow the division method for remaining coefficients
- The last value automatically becomes zero
- Write an equation using the obtained values
- Repeat the same process to find other values

**Examples:**

**Question1: Solve x ^{4}-2x^{3-}13x^{2}+14x+24=0 using a synthetic division method?**

Answer:

Given equation is x^{4}-2x^{3}-13x^{2}+14x+24=0

The factors of 24 are +-1, +-2, +-3, +-4, +-6, +-8, +-24

By substituting the -1 in the equation

(-1)^{4}-2(-1)^{3}-13(-1)^{2}+14(-1)+24=0

-1+2-13+-14+24=0

So -1 is the factor of the above equation and we can use synthetic division method

The coefficients of the equation are 1,-2,-13,14,24

Synthetic Division Method is

-1 1 -2 -13 14 24

-1 3 10 -24

1 -3 -10 24 0

(x+1)(x^{3}-3x^{2}-10x+24)=0

The coefficients of x^{3}-3x^{2}-10x+24 are 1, -3, -10, 24

Substitute 2 in the equation

(2)^{3}-3(2)^{2}-10(2)+24=0

8-12-20+24=0

So, 2 is another factor for the given equation

By Synthetic Division Method

2 1 -3 -10 24

2 -2 -24

1 1 -12 0

(x+1)(x-2)(x^{2}+x-12)=0

(x+1)(x-2)(x^{2}+4x-3x-12)=0

(x+1)(x-2)(x-4)(x+3)=0

The values of x are -1, 2, 4, -3.

**Question2: Solve x ^{3}-3x^{2}-4x+12=0 using factorization?**

Solution:

Given equation is x^{3}-3x^{2}-4x+12=0

x(x^{2}-3x)-4(x-3)=0

(x-3)(x^{2}-4)=0

The values of x are 3, -2, 2.

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**1. What is meant by Polynomial Equation Solver?**

Polynomial equation is defined as an algebraic equation which has variables, mathematical operators, coefficients, and constants. A polynomial equation has terms with different exponents. The higher exponent value is called the degree of an equation.

**2. What are the types of polynomial equations?**

The different types of polynomial equations are linear polynomial equations, cubic polynomial equations, quadratic polynomial equations, and so on.

**3. How do you solve a polynomial with 2 degree?**

The simple method to solve the quadratic polynomial equation is by finding the factors or using -b+-sqrt(b^{2}-4ac)/2a.

**4. Solve x ^{2}+3x+4=0?**

Find out the factors of the given equation. The equation can also be written as x^{2}+4x-x+4=0. Factors of the equation are (x-1)(x+4)=0. The solution is 1,-4.