Chapter 14, Problem 50SGR

To determine

To calculate: The factors of the polynomial expression $x^2+4x+4$ .

Answer to Problem 50SGR

The factors of the polynomial expression $x^2+4x+4$ are $x+2\text{and}x+2$ .

Explanation of Solution

Given Information:

The polynomial expression is $x^2+4x+4$ .

Calculation:

The given polynomial expression is $x^2+4x+4$ .

Split $4x$ into two parts such that their product is equal to the product of $x^2$ and 4.

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

Hence, the factors of the trinomial $x^2+4x+4$ are $x+2\text{and}x+2$ .