Question

Which of the following constants can be added to x^2-6x to form a perfect square trinomial

Answer 1

Answer:

9 is the constant that should be added to make the expression perfect square.

Step-by-step explanation:

The given expression is (x² - 6x)

We have to make this expression perfect square.

As we know the formula (a-b)² = a² + b² - 2ab

Now we will rewrite the expression given in the form of the formula.

[(x)² - 2 (3)x]

We find a as x' and b as 3

So by putting a = x and b = 3 in the formula we get

(x-3)² = x² + 3² -2(x)(3)

Therefore, 9 is the constant that should be added to make the expression perfect square.

Answer 2

Take half of the coeff. of x (which is 6), and then square the result:  3^2 = 9.

Then  x^2-6x  + 9 - 9, and

          x^2 - 6x + 9 is a perfect square trinomial.