Question

Determine whether the polynomial is a perfect square and if it is, factor it.

n^2 – 9n + 9

A.
is a perfect square: (n – 3)^2

B.
is a perfect square: (n – 9)^2

C.
is not a perfect square

D.
is a perfect square: (n + 3)^2

Answer 1

go to www.wolframalpha.com and maybe ull find ur answer it shows a bunch of data for that

Answer 2

B?

Answer 3

When you are factoring something of the form:
\[x^2 +ax + b^2\]
(like what you have here), it'll be a perfect square if a = 2b

Another way to think about this is, given the polynomial you have, can you find a number that, when squared, will equal the number with no x on it (in this case, 9), and when added to itself (or multiplied by 2), will equal the middle number with just x on it (in this case, -9)

If you can, it's a perfect square.

For instance:
\[x^2 +8x + 16\]
I need a number that when squared will equal 16, and when multiplied by 2 will equal 8.
That number is 4, so:
\[x^2+8x+16 = (x+4)^2\]

Can you find such a number for your polynomial?

Answer 4

\[\left( a+b \right)^2=a^2+2ab+b^2\]

Answer 5

\[\left( a-b \right)^2=a^2-2ab+b^2\]

Answer 6

well start by looking at 9

\[9 = (\pm 3)^2\]

and

\[x^2 = (\pm x)^2\]

so does the middle term have a value of \[2 \times (\pm 3) \times (\pm x)\]

if it does, you have a perfect square...

if it doesn't its not a perfect square

Answer 7

Im so confused..

Answer 8

It was C -.-

Answer 9

lol

Answer 10

I just randomly guessed and got it right ^.^

Answer 11

nice!