Problem

Find the last term to make the trinomial into a perfect square. If it is not an integer, write as a reduced fraction. \[ x^{2}+4 x+ \] Write the trinomial as a binomial squared writing reduced fractions (not decimals) as needed: Question Help: Video $D$ Post to forum

Solution

Step 1 :The trinomial is a perfect square if it is in the form of \((ax+b)^2\). Expanding this, we get \(a^2x^2 + 2abx + b^2\).

Step 2 :Comparing this with the given trinomial \(x^2 + 4x + c\), we can see that \(a^2 = 1\) (so \(a=1\)), \(2ab = 4\) (so \(b=2\)), and \(b^2 = c\) (so \(c=2^2 = 4\)).

Step 3 :Therefore, the last term that makes the trinomial a perfect square is 4.

Step 4 :Final Answer: The last term to make the trinomial into a perfect square is \(\boxed{4}\).

From Solvely APP
Source: https://solvelyapp.com/problems/17616/

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