What Is The Fully Factored Form Of $27x^3 + 7x^2$?Type Exponents In Your Answer Using The Caret Symbol. Example: If Your Answer Is $x^3(17x^2 + 9)$, You Would Type It As $x^{\wedge}3(17x^{\wedge}2 + 9)$ With No

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What is the Fully Factored Form of 27x^3 + 7x^2?

In algebra, factoring is a process of expressing a polynomial as a product of simpler polynomials. The fully factored form of a polynomial is a way of expressing it as a product of prime factors. In this article, we will explore the fully factored form of the polynomial 27x^3 + 7x^2.

The given polynomial is 27x^3 + 7x^2. To factor this polynomial, we need to find the greatest common factor (GCF) of the two terms. The GCF of 27x^3 and 7x^2 is 7x^2.

We can factor out the GCF, 7x^2, from both terms:

27x^3 + 7x^2 = 7x^2(3x + 1)

Now that we have factored out the GCF, we need to check if there are any other factors that can be factored out. In this case, we can see that the term 3x + 1 cannot be factored further.

Therefore, the fully factored form of 27x^3 + 7x^2 is 7x^2(3x + 1).

Factoring polynomials is an important skill in algebra and is used in a variety of applications, including solving equations and graphing functions. For example, if we have the equation 27x^3 + 7x^2 = 0, we can use the factored form to solve for x:

7x^2(3x + 1) = 0

We can set each factor equal to zero and solve for x:

7x^2 = 0 --> x = 0 3x + 1 = 0 --> x = -1/3

Therefore, the solutions to the equation are x = 0 and x = -1/3.

  • When factoring polynomials, it's often helpful to look for common factors first.
  • Use the distributive property to expand the polynomial and make it easier to factor.
  • Check your work by plugging the factored form back into the original polynomial.
  • Failing to factor out the GCF.
  • Not checking for other factors that can be factored out.
  • Not using the distributive property to expand the polynomial.

In conclusion, the fully factored form of 27x^3 + 7x^2 is 7x^2(3x + 1). Factoring polynomials is an important skill in algebra and is used in a variety of applications. By following the steps outlined in this article, you can master the art of factoring polynomials and solve equations with ease.
Q&A: Fully Factored Form of 27x^3 + 7x^2

In our previous article, we explored the fully factored form of the polynomial 27x^3 + 7x^2. In this article, we will answer some common questions that readers may have about factoring polynomials.

A: The GCF of 27x^3 and 7x^2 is 7x^2.

A: To factor out the GCF, you can divide both terms by the GCF. In this case, you can divide 27x^3 by 7x^2 to get 3x, and divide 7x^2 by 7x^2 to get 1. Therefore, the factored form is 7x^2(3x + 1).

A: No, the term 3x + 1 cannot be factored further.

A: The fully factored form of 27x^3 + 7x^2 is 7x^2(3x + 1).

A: To use the factored form to solve equations, you can set each factor equal to zero and solve for x. For example, if we have the equation 27x^3 + 7x^2 = 0, we can set each factor equal to zero and solve for x:

7x^2 = 0 --> x = 0 3x + 1 = 0 --> x = -1/3

A: Some common mistakes to avoid when factoring polynomials include:

  • Failing to factor out the GCF.
  • Not checking for other factors that can be factored out.
  • Not using the distributive property to expand the polynomial.

A: To check your work when factoring polynomials, you can plug the factored form back into the original polynomial and simplify. If the factored form is correct, the simplified expression should be equal to the original polynomial.

A: Some tips and tricks for factoring polynomials include:

  • Looking for common factors first.
  • Using the distributive property to expand the polynomial and make it easier to factor.
  • Checking your work by plugging the factored form back into the original polynomial.

In conclusion, the fully factored form of 27x^3 + 7x^2 is 7x^2(3x + 1). By following the steps outlined in this article, you can master the art of factoring polynomials and solve equations with ease.