Chapter 12, Problem 40CLR

To determine

To find: The factor of the given polynomial and the if it cannot be factored thaw write prime.

Answer to Problem 40CLR

The factored form of the polynomial is ${\left(7r+4s\right)}^2$ .

Explanation of Solution

Given:

The given polynomial is $49r^2+56+16s^2$ .

Calculation:

Consider the given polynomial is,

  $49r^2+56+16s^2$

Then, the solution is,

  $49r^2+56+16s^2$

The first term and the last term of the above expression is the perfect square and the factored form of the polynomial is,

  $\begin{array}{c}49r^2+56rs+16s^2={\left(7r\right)}^2+2\left(7r\right)\left(4s\right)+{\left(4s\right)}^2\\ ={\left(7r+4s\right)}^2\end{array}$