trinomials 9.1 11

Question

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.



x squared+7x+?___

 

What is the constant term?

What is the factored form of the trinomial?

Answer 1

What you want to do is complete the square of a form

 

ax^2 + bx

 

by adding some constant c, which may be shown to be:

 

c = b^2 / 4a

 

The polynomial then becomes

 

ax^2 + bx + b^2 / 4a

 

which then factors to

 

ax^2 + bx + b^2 / 4a = a(x + b/2a)^2

 

a = 1

b = 7

c = b^2 / 4a = 7^2 / (4*1) = 49/4

 

Test it:

 

a[x + b/(2a)]^2 = (1)[x + 7/(2*1)]^2 = (x + 7/2)^2 = x^2 + 2(7/2)x + (7/2)^2 = x^2 + 7x + 49/4

 

 

 

 

Answer 2

Hello Shawn,

The constant term is (7/2)² = 49/4

Now, your Trinomial should have three terms, x²+7x+49/4 and called a perfect squared trinomial because the added constant made it perfect to be squared like this: (x+7/2)²

and that is the factored form of the trinomial. Just a note over here, that you can write the factor form as

(x+7/2)(x+7/2) instead, if it is going to clarify it more for you to see the factors.

I hope that answers your question.

To summarize, always, when the coefficient for x² is 1, to complete a trinomial to a perfect square: use the coefficient next to the x variable, i.e. the second term coefficient, divide it over 2 then square the result.

Please, ask as much as you can to understand more and feel free to seek tutoring.

Bader A.