Taking Out Coefficient

Taking out coefficient is a process of factoring out the greatest common factor of a polynomial. It is an important concept in algebra and is used to simplify expressions and solve equations. Let us understand it in detail.

Definition:

The greatest common factor (GCF) of a polynomial is the largest monomial that divides all the terms of the polynomial without leaving a remainder.

Example:

The GCF of the polynomial 6x^3 + 12x^2 + 18x is 6x.

Steps to Take Out Coefficient:

Step 1: Identify the terms of the polynomial and find the GCF of the coefficients.

Step 2: Divide each term of the polynomial by the GCF of the coefficients.

Step 3: Write the GCF of the coefficients in front of the parentheses, and write the simplified polynomial inside the parentheses.

Example:

Take out the GCF of the polynomial 4x^2 + 8x^3.

Step 1: The coefficients of the polynomial are 4 and 8. The GCF of the coefficients is 4.

Step 2: Divide each term of the polynomial by 4. We get:

4x^2/4 + 8x^3/4 = x^2 + 2x^3/4

Step 3: Write the GCF of the coefficients in front of the parentheses and write the simplified polynomial inside the parentheses. We get:

4(x^2 + 2x^3/4)

This is the factored form of the polynomial.

Uses of Taking Out Coefficient:

1. Simplify expressions: Taking out the GCF of a polynomial simplifies the expression by reducing the number of terms.

2. Solve equations: Taking out the GCF of a polynomial helps in solving equations by making the expression easier to work with.

3. Finding common factors: Taking out the GCF of two or more polynomials helps in finding common factors of the polynomials.

Conclusion:

Taking out coefficient is an important concept in algebra that helps in simplifying expressions and solving equations. It is a simple process that involves identifying the terms of the polynomial, finding the GCF of the coefficients, dividing each term of the polynomial by the GCF, and writing the GCF in front of the parentheses and the simplified polynomial inside the parentheses.

3x
coefficient of this is 3