Advanced Algebra 2 problem

[acunaduran]

Can someone please help with the following problem?

x squared + 21x + __ =

Instructions are to complete the square.

Thanks!

 

[mmm4444bot]

x squared + 21x + __ =

Instructions are to complete the square.

I'm guessing that you're supposed to fill in the blank (on the left) and write the factorization of the resulting polynomial (on the right).

In other words, I'm interpreting the posted instruction to mean, "Fill in the blank to create a perfect-square trinomial on the lefthand side, and write the factorization for this polynomial on the righthand side".

For this, there is a simple rule in "Completing the Square".

Given a binomial of the form: x^2 + Bx

we add (B/2)^2, to form a perfect-square trinomial.

This polynomial always factors as (x + B/2)^2.

EG:

Form a perfect-square trinomial out of the following binomial and write its factorization.

x^2 + 7x

This binomial is of the form: x^2 + Bx, where B = 7.

We need to add (B/2)^2.

(B/2)^2 = (7/2)^2 = 49/4

The factorization is (x + B/2)^2

The answer is:

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

Can you proceed now?

Please share your work or thoughts, if you need more help with this exercise.

Cheers ~ Mark