Given the following perfect square trinomial, fill in the missing term.

x^2 − 16x + ____

Question

Given the following perfect square trinomial, fill in the missing term. 

x^2 − 16x + ____

imstuck · Answer

This is another way of asking you to complete the square.  Do you know how?

anonymous · Answer

Not a clue.

anonymous · Answer

A perfect square trinomial has one factor that is squared.

For example: $$(x+4)^{2}\rightarrow(x-4)^{2}\rightarrow (x+1)$$

And so on. Each of those is a perfect square trinomial because it can be written with the same factor twice

(x+4)(x+4)

(x-4)(x-4)

(x+1)(x+1)

All of that being said, we are looking for what factor we can multiply by the same factor again to get the beginning part to be $$x ^{2}-16x...$$

imstuck · Answer

Take half the x term and square it.  -16/2 = -8.  -8 squared is 64.  So add 64 in and then you have a perfect square binomial, like this:$$x ^{2}-16x+64 = (x-8)^{2}$$

anonymous · Answer

The (x+1) example up at the top is supposed to be squared like $$(x+1)^{2}$$

imstuck · Answer

The coefficient in front of the x^2 term HAS TO BE A 1, then you will always take half the x term and square it. THat's how to complete the square.

anonymous · Answer

I'm really confused

imstuck · Answer

about what?

anonymous · Answer

So, we ask ourselves, what factor can be added together with itself to give us -16. That would be -8.

So we know (x-8)(x-8) would give us $$x ^{2}-16x... $$

Then what @BassCatcher15 ?

anonymous · Answer

These are all just examples of perfect square trinomials...

$$(x+1)^{2}\rightarrow(x-5)^{2}\rightarrow(x+13)^{2}\rightarrow(x+4)^{2}$$

nikato · Answer

complete the square

normally you see trinomials written like this
$$ax ^{2}+bx+c$$

but right now you are only given 
$$ax ^{2}+bx$$
and you're trying to find c

anonymous · Answer

64?

anonymous · Answer

You got it.

nikato · Answer

to find c, 
divide b by 2 and square it

so
$$(\frac{ b }{ 2 })^{2}=c$$

anonymous · Answer

Given the following perfect square trinomial, fill in the missing term. (Do not type the variable in the blank.) 

4x^2 + ___x + 49

This would be 7^2 right?

anonymous · Answer

@nikato

anonymous · Answer

@Cosmichaotic

nikato · Answer

7^2 is not right

anonymous · Answer

Then can you explain how to do this?

nikato · Answer

can you think of a number that equals 49 when its squared?

anonymous · Answer

7

nikato · Answer

yes. and the same with 4x^2.

what squared equals 4x^2

anonymous · Answer

jeez louise
what is half of sixteen?

anonymous · Answer

8

anonymous · Answer

yes 
what is eight squared?

anonymous · Answer

64

anonymous · Answer

yes
that is your answer 

done
finished
stick a fork in it

anonymous · Answer

Haha.  Thanks!

anonymous · Answer

yw

nikato · Answer

i thought we were done with that question already

anonymous · Answer

I thought so too.  Did the next question not post?

anonymous · Answer

Given the following perfect square trinomial, fill in the missing term. (Do not type the variable in the blank.) 

4x^2 + ___x + 49

nikato · Answer

yea. i was trying to help you.

so what number squared equals 4x^2

anonymous · Answer

16 right?

nikato · Answer

no.
2x
because (2x)^2 = 4x^2
16=4^2

anonymous · Answer

Ohhhh okay!

nikato · Answer

so if we were to factor this PERFECT trinomial it would be

$$(2x ^{2}+7)^{2}$$

mathstudent55 · Answer

$4x^2 + \_\_\_\_x + 49$

The $4x^2$ term comes form $2x \times 2x$ 
The $49$ term comes from $7 \times 7$

Then the trinomial must come from 

$(2x + 7)(2x + 7) $

Let's square $(2x + 7):$

$ (2x + 7)^2 = 4x^2 + 28x + 49$

Now you see clearly what the x term is.

anonymous · Answer

So the blank is 7?

mathstudent55 · Answer

Look at my last line. What's the coefficient of the x term? It's 28.

anonymous · Answer

Oh okay.  Thanks!

mathstudent55 · Answer

$4x^2 + \_\_\_\_x + 49$

$4x^2 + \color{red}{28}x + 49$