Question

Name: Factoring with GCF Factor the common factor out of each expression. 8+6x^(4)

Answer 1

Expression 8 + 6x⁴ is factored by taking out the greatest common factor, which is 2, resulting in 2(4 + 3x⁴).

Step-by-step explanation:

The expression given is 8 + 6x4. To factor the common factor out of this expression, we first look for any common variables or numbers that are in each term. Since there are no common variables and the numbers 8 and 6 only share a factor of 2, we can't factor out a variable, but we can pull out the 2 as the greatest common factor (GCF).

Therefore, the factored expression would be:

2(4 + 3x4)

To do this, we divide each term by 2:

8 ÷ 2 = 4

6x4 ÷ 2 = 3x4

Always remember to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable

Answer 2

The common factor of the expression 8 + 6x^4 is 2.

Step-by-step explanation:

To factor out the greatest common factor (GCF) from an expression, identify the largest number or term that can be divided evenly into each term. In this case, the GCF of 8 and 6x^4 is 2. When factoring out 2, divide each term by 2: 8 ÷ 2 = 4, and 6x^4 ÷ 2 = 3x^4. Therefore, factoring out 2 from both terms results in the expression 2(4 + 3x^4).

Factoring allows simplification of expressions by breaking them down into their common components. By factoring out the GCF, in this case, the numerical coefficient 2, the expression becomes more manageable and easier to work with.

This process is crucial in algebraic manipulation, aiding in solving equations, identifying patterns, and simplifying complex expressions. In this instance, factoring out the common factor 2 from 8 + 6x^4 simplifies the expression to 2(4 + 3x^4), which showcases the shared factor in both terms.