Question

Given the following perfect square trinomial, fill in the missing term. (Do not type the variable in the blank.) (2 points)

4x2 + ___x + 49

Answer 1

This is a perfect square trinomial of the form `(ax + b)² = a²x² + 2abx + b²`.

In this case, we have `4x² + ___x + 49`.

We can take half of the middle term and square it to find the missing term.

The middle term is `2abx`, so `2ab = x`.

We can see that `a = 2` and `b = 7`, so `2(2)(7) = 28`.

Therefore, the missing term is `28x²`.

So the complete trinomial is `4x² + 28x + 49`.

Step-by-step explanation: