Chapter 7, Problem 30CR

To determine

Factor the expression, $28x-42$

Answer to Problem 30CR

The factored form of $28x-42$ is $7\left(4x-6\right)$ .

Explanation of Solution

Given Information:

The expression: $28x-42$

Concept Used:

• The GCF (Greatest Common Factor) of a list of integers is the largest integer that is a factor of all the integers in the list.
• The GCF (Greatest Common Factor) of a list of common variable factors raised to powers is the variable raised to the smallest exponent in the list.
• Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

To factor the given polynomial, we will factor out the GCF from each term and write the remaining factors of each term as a product of this GCF.

Here observe that both the terms have a common factor $7$ . So we factor out the common factor from each term and write the remaining factors of each term as a product of this factor. So using the distributive property, we can write it as

  $\begin{array}{l}28x-42\\ =7\left(4x-6\right)\end{array}$

Thus, the factored form of $28x-42$ is $7\left(4x-6\right)$ .