Question

Consider the expression\[x^2 + 18x + \boxed{\phantom{00}}. \] find all possible values for the missing number that make this expression the square of a binomial.

Answer 1

The possible values for the missing number that make the given expression the square of a binomial is; 81

Binomial Expression

We are given the expression;

x² + 18x

• Now, if we consider the binomial; x ± b

Squaring that gives us;

x² ± 2ax + b²

Comparing this expression to the one we are given we can say that;

±2ax = 18x

±a = 18/2

a = ±9

Thus,we will have;

(x + 9)² as our expression which is;

x² + 18x + 81

Therefore, the missing number is 81.

Read more on binomial expression at; brainly.com/question/14968861