Chapter 9.5, Problem 1P

Find the value of $c$ such that each expression is a perfect-square trinomial.

$x^2+4x+c$

To determine

To find : the value of $c$ such that each expression is a perfect-square trinomial

Answer to Problem 1P

The value of $c$ is 4

Explanation of Solution

Given information :

The expression is

  $x^2+4x+c$

Formula used :

  $a^2+2ab+b^2={\left(a+b\right)}^2$

Calculation :

The solution of the expression is

  $\begin{array}{l}{x}^2+4x+c\\ ={\left(x\right)}^2+2\cdot x\cdot 2+{\left(2\right)}^2\\ ={\left(x+2\right)}^2\end{array}$

Therefore, the value of $c$ is 4 because that makes a perfect-square trinomial.

Hence, the value of $c$ is 4.