Chapter 14.7, Problem 19HP

To determine

Explain how the Distributive Property is used to factor polynomials.

Answer to Problem 19HP

Distribution property is used to multiply the sub-polynomial expression to form a complete polynomial expression.

Explanation of Solution

Distribution property states that the multiplication of two or more polynomial gives the same result as the addition of the multiplication of each of the terms of the polynomials.

For example:

  $\begin{array}{c}9x+15=3\times 3x+3\times 5\\ =3\left(3x+5\right)\end{array}$

Similarly, another example:

  $\begin{array}{c}36mn-11m{n}^2=mn\times 36-mn\times 11n\\ =mn\left(36-11n\right)\end{array}$

Hence, distribution property is used to multiply the sub-polynomial expression to form a complete polynomial expression.