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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

Respuesta :

Answer:

[tex]\frac{49}{4}[/tex]

[tex](x+\frac{7}{2} )^{2}[/tex]

Step-by-step 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 [tex]\frac{7}{2}[/tex]

on squaring it we get

therefore here  number with second term is 7 ,Dividing 7 by 2 ,we get [tex]\frac{49}{4}[/tex]

So expression is

[tex]x^2+7x+\frac{49}{4}[/tex]

[tex](x+\frac{7}{2} )^{2}[/tex]

kudzordzifrancis

Answer:

i. [tex](\frac{7}{2} )^2[/tex]

ii. [tex](x+\frac{7}{2})^2[/tex]

Step-by-step explanation:

The give expression is

[tex]x^2+7x+\:----[/tex]


We need to find half the coefficient of [tex]x[/tex] and the square the result.



Half of [tex]7[/tex] is [tex]\frac{7}{2}[/tex].


When we square it, we get;

[tex](\frac{7}{2} )^2[/tex]


Hence we add [tex](\frac{7}{2} )^2[/tex] to obtain;

[tex]x^2+7x+(\frac{7}{2})^2[/tex]


The expression as a binomial squared is


[tex](x+\frac{7}{2})^2[/tex]



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