Question

If x² + bx is a binomial, then by adding (b/2)², which is the square of half of the coefficient of x, a perfect square trinomial will result in _____.

Answer 1

Adding the square of half the coefficient of x to a binomial will result in a perfect square trinomial.

Step-by-step explanation:

Adding (b/2)² to a binomial x² + bx will result in a perfect square trinomial.

Let's consider an example to see how this works:

Suppose we have the binomial x² + 4x. The coefficient of x is 4, so half of the coefficient is 2. We square 2, which gives us 4. By adding 4 to the binomial, we get the perfect square trinomial x² + 4x + 4.

Therefore, by adding (b/2)² to a binomial, we always get a perfect square trinomial.