Question

Complete the square for each expression. Write the resulting expression as a binomial. x^2+26x+____

Answer 1

Given the expression written in the following form:

$ax^2+bx+c$

You can complete the square for the expression by following these steps:

1. You must take the coefficient "b", divide it by 2 and then you must square it:

$(\frac{b}{2})^2$

For this case you can identify that "b" is:

$b=26$

Therefore:

$(\frac{b}{2})^2=(\frac{26}{2})^2=(13)^2=169$

2. Complete the square by adding 169 to the expression given:

$=x^2+26x+169$

3. Factor it in order to express it as a binomial.

The answer is:

$=(x+13)^2$