21 Determine the constant that should be added to the binomi

#21: Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then, write and factor the trinomial. x²+20x Answer: What is the constant that should be added to the binomial so that it becomes a perfect square trinomial?

Solution

Given : x^2 + 20x

Let the constant be \'y^2\' . So, trinomial : x^2 + 20x +y^2

We use the formula for perfect square : (a +b)^2 = a^2 +b^2 +2ab

Now we compare our binomial with this formula:x =a ; 2ab =20x

2b = 20 ; b= 10

So, y = 10 ; y^2 =100

So, x^2 +20x +100 = (x +10)^2 perfect square trinomial

So, 100 is the constant to be added