Chapter 8.2, Problem 2CYU

To determine

The use of Distributive Property to factor the given polynomial.

Answer to Problem 2CYU

  $2c\left(7c+1\right)$

Explanation of Solution

Given:

The given polynomial is:

  $14c^2+2c$

Calculation:

The given polynomial can be factorized using Distributive Property as:

Write the factors of each term:

  $\begin{array}{l}14c^2\\ =2\times 7\times c\times c\\ 2c\\ =2\times c\end{array}$

Now, take out the common factors from the factors of each term of the polynomial to find the GCF:

  $GCF=2c$

Write each term as the product of GCF and the remaining factors. Finally use the Distributive Property to factor out the GCF.

  $\begin{array}{l}14c^2+2c=2c\left(7c\right)+2c\left(1\right)\\ 14c^2+2c=2c\left(7c+1\right)\end{array}$