Question

I know how to identify perfect square trinomials, but how do I find a missing third term?

Answer 1

For example, if we had 9x^2 - 6x + ? what would the third term be?

Answer 2

is there an answer choice

Answer 3

No, I'm just trying to understand this concept :)

Answer 4

oh i will try

Answer 5

give me one sec

Answer 6

Okay

Answer 7

I know that (a + b)^2 = a^2 + 2ab + b^2

Answer 8

whats after 6x

Answer 9

Factor out a 9.
\[9(x^{2} - \frac{2}{3}x + C)\]

C should be (b/2)^2 = (2/6)^2 = (1/3)^2 = (1/9)

9(x^2 - (2/3)x + (1/9))

= \[9x^2 - 6x + 9\]

Answer 10

That's the question, you have to find whats after 6x

Answer 11

@iPwnBunnies that's incorrect, I know the answer but I don't know how they got it

Answer 12

9 (x - (1/3))^2

Answer 13

it's 1

Answer 14

Sorry, I'm sorta thinking out loud.

Answer 15

Yeah, it might be 1.

Answer 16

@iPwnBunnies was right with that formula. He just did that last multiplication wrong.

9* (1/9) = 1 and not 9 as he said.

Answer 17

Given the perfect square trinomial 9x^2 - 6x + __.

Since we were told this is a perfect square trinomial, we know that the last term equals b2, and the coefficient of the middle term equals 2ab. We can find the value of “a” by taking the square root of the first term, 9x^2.

√(9x^2)=3x

So, the coefficient of the middle term 2ab = 2(3x)(b) = 6xb.

But we know the value of the middle term is 6x, so we set 6x = 6xb, and solve for b.

b = 1

The last step is to square the b term. (1)(1) = 1.

Therefore, the perfect square trinomial is 9x2 - 6x + 1.

Answer 18

But I don't know what they're really talking about, it confuses me...

Answer 19

Ahh, you're right. Thanks Diogo.

Answer 20

@LearningIsAwesome , follow @iPwnBunnies 's formula.
Its as simple as that :)

Answer 21

I still don't get it though, can we put it in more practical terms?

Answer 22

More practical terms? .-. Math expressions are the practical terms, right? When you wanna find the perfect square trinomial of something like this:

\[x^{2} + 10x + C\]
C will be equal to (10/2)^2. This little formula creates the constant for a perfect square trinomial.

Answer 23

\[(\frac{10}{2})^{2} = 25\]

\[x^{2} + 10x + 25 = (x+5)^{2}\]

Answer 24

Why divided by 2?? Where'd the 2 come from?

Answer 25

ok, basically you just need to solve whats inside the root of the solving formula.



x = [-b+/-sqrt(b^2-4ac)]/2a


To solve that you just need to know that the square root must be positive or 0.

In this case you want it to be 0, so



sqrt(b^2-4ac)=0
sqrt(6^2-4*9*c)=0
6^2-4*9*c=0
6^2=4*9*c
36=36*c
c=1

Answer 26

I'm still so confused... :/

Answer 27

ok to answer your question, if you have a polynomial of 9x^2 - 6x and you want the third term, you would have to complete the square.

Answer 28

Right and a^2 + 2ab + b^2

Answer 29

Like this: you take out a 9, cuz you can only complete the square on a polynomial that has a 1 as its leading coefficient. So far it looks like this: