Chapter 8, Problem 45SGR

To determine

To factorize the given expression

Answer to Problem 45SGR

  $(3r^2-p)(r-4)$

Explanation of Solution

Given:

Expression: $3r^3-12r^2+4p-pr$

Concept used:

Distributive property: $a(b+c)=a\cdot b+a\cdot c$

Calculation:

Consider the expression $3r^3-12r^2+4p-pr$ ,

  $\begin{array}{l}\Rightarrow 3r^3-12r^2+4p-pr\\ \Rightarrow 3r^2(r-4)-p(r-4)\end{array}$

Applying the distributive property,

  $\begin{array}{l}\Rightarrow 3r^2(r-4)-p(r-4)\\ \Rightarrow (3r^2-p)(r-4)\end{array}$

Conclusion:

Therefore, the factors of the given expression are $(3r^2-p)(r-4).$