Factor out the greatest common factor polynomial calculator

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.

Solution

Your input: factor $$$x^{2} + 4 x + 3$$$.

To factor the quadratic function $$$x^{2} + 4 x + 3$$$, we should solve the corresponding quadratic equation $$$x^{2} + 4 x + 3=0$$$.

Indeed, if $$$x_1$$$ and $$$x_2$$$ are the roots of the quadratic equation $$$ax^2+bx+c=0$$$, then $$$ax^2+bx+c=a(x-x_1)(x-x_2)$$$.

Solve the quadratic equation $$$x^{2} + 4 x + 3=0$$$.

The roots are $$$x_{1} = -1$$$, $$$x_{2} = -3$$$ (use the quadratic equation calculator to see the steps).

Therefore, $$$x^{2} + 4 x + 3 = \left(x + 1\right) \left(x + 3\right)$$$.

$$\color{red}{\left(x^{2} + 4 x + 3\right)} = \color{red}{\left(x + 1\right) \left(x + 3\right)}$$

Thus, $$$x^{2} + 4 x + 3=\left(x + 1\right) \left(x + 3\right)$$$.

Answer: $$$x^{2} + 4 x + 3=\left(x + 1\right) \left(x + 3\right)$$$.

In mathematics, GCF stands for Greatest Common Factor where the largest number that divided evenly into the given number. Whereas the factoring out GCF from the polynomials is the product of all their common prime factors.

For instance, the GCF of 2x and 4x^2 is 2x.

Factoring Polynomials Formulas

1. mx+my=m(x+y)

2. x2-y2=(x-y)(x+y)

3. x3-y33=(x-y)(x2+xy+y2)

4. x3+y3=(x+y)(x2-xy+y2)

5. (x+y)2=x2+2xy+y2

6. (x-y)2=x2-2xy+y2

7. (x+y)3=x3+y3+3xy(x+y)

8. (x-y)3=x3-y3-3xy(x-y)

9. (x+y+z)2=x2+y2+z2+2xy+2yz+2zx

How to Solve the Factoring out the Greatest Common Factor of a Polynomial?

The best way to grasp the concept of how to factor out common factors is by understanding the distributive property. Here we will be using this property to Factoring out the greatest common factor (GCF) of a Polynomial. The formula for distributive property is a(b+c)=ab+ac. The remaining process of factoring out GCF from polynomials is discussed below so refer to the simple steps provided here:

• Find the GCF of all the terms in the polynomial.
• Prove each term as a product of the GCF and another factor.
• Apply the distributive property to factor out the GCF from the polynomial.

Try Factor a Polynomial by Finding Its Greatest Common Factor by hand following the above steps and also verify your results from the factorpolynomials.com provided Factor out the GCF from the Polynomial Calculator in no time.

Example:

Solve the factoring GCF polynomial x^3-1, x+1 and verify it using Factor the polynomial by its greatest common monomial factor calculator.

Solution:

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.

1. How do you factor a polynomial by its greatest common monomial factor?

To find the greatest common factor (GCF) between monomials, take each monomial and write its prime factorization. Then, identify the factors common to each monomial and multiply those common factors together.

2. How do you factor out the GCF of polynomial easily?

You can factor out the GCF of polynomial easily by using the online calculator tool ie., factor out GCF from Polynomial Calculator.

3. Where can I find the accurate results of factoring out the greatest common factor from polynomials?

You can find the accurate results of factoring out the greatest common factor from polynomials from our page by using our handy tool.

4. Which is the best website that provides mathematical calculators to solve polynomials?

The best website that provides trusted mathematical calculators to determine the polynomial calculations is factorpolynomials.com

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