Find the term that should be added to the expression to form a perfect square trinominal. Write the resulting perfect square trinomial in factored form.
x^2+5x
To find the term that should be added, we take half of the coefficient of the x term and square it.
Half of 5 is 2.5, and when we square it we get 6.25.
So the term that should be added to the expression is 6.25.
The resulting perfect square trinomial in factored form is:
(x + 2.5)^2 or (x + 2.5)(x + 2.5)
To form a perfect square trinomial, we need to add the square of half the coefficient of the middle term squared.
The coefficient of the middle term is 5. Half of 5 is 2.5, and its square is 6.25.
To make x^2 + 5x a perfect square trinomial, we add 6.25.
The resulting perfect square trinomial in factored form is:
(x + 2.5)^2
To find the term that should be added to the expression to form a perfect square trinomial, we need to take half of the coefficient of x (in this case, 5) and square it.
Half of 5 is 5/2, and squaring this gives us (5/2)^2 = 25/4.
Therefore, the term that should be added to the expression x^2 + 5x to form a perfect square trinomial is 25/4.
To write the resulting perfect square trinomial in factored form, we start with the original expression and add the term we found:
x^2 + 5x + 25/4
Now, to factor this, we look for a perfect square trinomial pattern:
(a + b)^2 = a^2 + 2ab + b^2
In our case, a is x and b is 5/2. So, we have:
(x + 5/2)^2
Therefore, the resulting perfect square trinomial in factored form is (x + 5/2)^2.