Question

Find the number that must be added to each expression to form a perfect square trinomial. Then write the trinomial as a binomial squared.

Answer 1

49/4 is the number.

Explanation:

We have given the expression:

x²+7x+?

We have to find the number that must be added to form a perfect square trinomial.

(x+7/2)² = x+2(x)(7/2)+(7/2)²

(x+7/2)²

To form the expression perfect square 49/4 is added.

(x+7/2)² = x+2(x)(7/2)+(7/2)²= x+7x+49/4

Answer 2

Hello!

The answers are:

a)
`(49)/(4)`

b)
`(x+(7)/(2))^(2)`

Why?

First, we need to know that for this case:

`a=1\\2ab=7`

So,

`b=(7)/(2)`

`b^(2) =((7)/(2))^(2)=(49)/(4)`

We must add
`(49)/(4)` to the expression in order to form a perfect square trinomial,

`x^(2) +7x+(49)/(4)`

Writing the trinomial as a binomial square:

`(x+(7)/(2))^(2)=x^(2)+2*(7)/(2)*x+((7)/(2))^(2)=x^(2) +7x+(49)/(4)`

Have a nice day!