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.

x^2+7x+____

( )^2

Answer 1

i.
`((7)/(2) )^2`

ii.
`(x+(7)/(2))^2`

Explanation:

The give expression is

`x^2+7x+\:----`

We need to find half the coefficient of
`x` and the square the result.

Half of
`7` is
`(7)/(2)`.

When we square it, we get;

`((7)/(2) )^2`

Hence we add
`((7)/(2) )^2` to obtain;

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

The expression as a binomial squared is

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

Answer 2

`(49)/(4)`

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

Explanation:

We always divide by 2 to the number in front of second term of the trinomial [ that is term with x ]

and then we add the square of such obtained number in order to make it perfect

therefore here number with second term is 7 ,Dividing 7 by 2 ,we get
`(7)/(2)`

on squaring it we get

therefore here number with second term is 7 ,Dividing 7 by 2 ,we get
`(49)/(4)`

So expression is

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

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