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:

`((b)/(2))^2`

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

`b=26`

Therefore:

`((b)/(2))^2=((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`