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

Question

pls i didn't know my question could u help me with that? thank u 

Answer 1

A Perfect Square Trinomial is a polynomial expression such that its factors is a perfect square. 

 

For Example:

 

x^2+12x+36 can be factored as (x+6)^2.

 

Notice that the x^2 is the square of x, 36 is 6^2 and the middle term is 2*x*6. 

 

Getting to your question,

 

we need to add a constant to the end of your expression such that it becomes a Perfect Square Trinomial.

 

Since we know the middle and first terms, lets use the above mention patter that the middle term should be

twice the square root of the first term and the constant.

 

-x=2*x*Constant -> Constant=-1/2

 

With this constant, we can write the PST as (x-1/2)^2.

 

Expand this to find that;

 

(x-1/2)^2=x^2-x-(1/4).

 

So you must add -1/4 to your expression.

Answer 2

A perfect square trinomial is a trinomial that is equivalent to a binomial squared.

 

(x+5)² = (x+5)(x+5) = x²+ 5x+5x+25 = x²+10x + 25

(x-7)² = (x-7)(x-7) = x² -7x-7x+49 = x²-14x+49

 

So the middle term of the trinomial, or the x term, is double the original and the final term or the end term is the square of the original.

5....doubled is 10 and squared is 25....look at the first trinomial above.

-7....doubled is -14 and squared is 49.....look at the second trinomial above.

 

So if you have x² + 18x and need to make it a perfect square trinomial, to get 18, you must have doubled 9. So this comes from (x+9)²....which expanded would be x²+18x +81......so you need to add 81.

 

In genereal, if you take 1/2 the middle term, then square that result, that's the number you need to add.

 

So for your example, x²-x, the coefficient of the x term is -1. 1/2 of that would be -1/2. Squaring that you would get 1/4. So you need to add 1/4 in order to make this a perfect square trinomial./

 

Hope this explanation helped.