Chapter 8.7, Problem 42PPS

To determine

To factor the given polynomial

Answer to Problem 42PPS

  $(15m+12)(m-5)(m+5)$

Explanation of Solution

Given:

Polynomial: $15m^3+12m^2-375m-300$

Concept used:

Finding common factor in each term and factoring using grouping method.

Calculation:

Consider the given polynomial,

  $\Rightarrow 15m^3+12m^2-375m-300$

Group the like terms and find common factor.

  $\Rightarrow (15m^3-375m)+(12m^2-300)$

Find out common terms in the above expression.

  $\begin{array}{l}\Rightarrow (15m^3-375m)+(12m^2-300)\\ \Rightarrow 15m(m^2-25)+12(m^2-25)\end{array}$

Here, $(m^2-25)$ is a common factor.

  $\Rightarrow (15m+12)(m^2-25)$

Further, $(m^2-25)$ can be factored as,

  $\begin{array}{l}$ \Rightarrow (m^2-25)=({(m)}^2-5^2)=(m-5)(m+5)$\because a^2-b^2=(a+b)(a-b)\end{array}$

Therefore, the polynomial can be factorised as,

  $\Rightarrow (15m+12)(m-5)(m+5)$

Conclusion:

Therefore, the polynomial is factored as $(15m+12)(m-5)(m+5).$