Chapter 8.5, Problem 49PPE

To determine

To calculate: The factor of $x^2+27x+50$

Answer to Problem 49PPE

  $(x+2)(x+25)$

Explanation of Solution

Given information: The expression $x^2+27x+50$

Calculation:

  $\begin{array}{l}{x}^2+27x+50\\ =x^2+(25+2)x+50[\because 50=25\times 2\text{and}\text{ 27}=25+2]\\ =x^2+25x+2x+50\\ =(x^2+25x)+(2x+50)\\ =x(x+25)+2(x+25)\\ =(x+2)(x+25)\end{array}$

Thus, $x^2+27x+50=(x+2)(x+25)$