(07.03 MC) Given the following perfect square trinomial, find the missing term: __ x^2+40x+100 1 1 2 4 10

## Step 1<br />A perfect square trinomial is a trinomial that can be factored into the square of a binomial. In this case, we are given the trinomial \(x^{2}+40x+100\), and we are asked to find the missing term that would make this a perfect square trinomial.<br /><br />## Step 2<br />The general form of a perfect square trinomial is \(a^{2}+2ab+b^{2}\), which can be factored into \((a+b)^{2}\).<br /><br />## Step 3<br />In our given trinomial, \(x^{2}\) corresponds to \(a^{2}\), and \(100\) corresponds to \(b^{2}\). Therefore, \(a\) is \(x\) and \(b\) is \(10\).<br /><br />## Step 4<br />The middle term of the trinomial, \(40x\), corresponds to \(2ab\) in the general form. Therefore, we can set up the equation \(2ab = 40x\).<br /><br />## Step 5<br />Substituting \(a = x\) and \(b = 10\) into the equation, we get \(2*10*x = 40x\), which simplifies to \(20x = 40x\).<br /><br />## Step 6<br />Solving for \(x\), we find that \(x = 2\). Therefore, the missing term in the trinomial is \(2\).