Question

Which constant should be added to the binomial x²-10x so that it becomes a perfect square trinomial?

a. 5
b. 100
c. 10
d. 25

Answer 1

To make x²-10x a perfect square trinomial, add 25 to it, resulting in x²-10x+25 which factors into (x-5)², representing a perfect square.

Step-by-step explanation:

The constant that should be added to the binomial x²-10x to make it a perfect square trinomial can be found by taking half of the coefficient of x, squaring it, and adding it to the expression. In this binomial, the coefficient of x is -10. We halve this to get -5, and then square -5 to obtain 25. So, by adding 25 to x²-10x, we get x²-10x+25, which is a perfect square trinomial because it can be factored as (x-5)².

Step-by-Step Solution:

1. Identify the coefficient of x, which is -10.
2. Divide this by 2 to get -5.
3. Square -5 to get 25.
4. Add 25 to the binomial to obtain x²-10x+25.
5. Recognize that x²-10x+25 is a perfect square since it can be factored as (x-5)².

Therefore, the correct answer is d. 25.