Which polynomial is a perfect square trinomial?

36x^2 − 18x − 9

4a^2 − 28a − 49

25b^2 − 40b + 16

4x^2 − 6x + 9

Question

Which polynomial is a perfect square trinomial?

 36x^2 − 18x − 9

 4a^2 − 28a − 49

 25b^2 − 40b + 16

 4x^2 − 6x + 9

mathstudent55 · Answer

Do you understand my explanation above?

anonymous · Answer

nooo .. :O

mathstudent55 · Answer

Ok, let's do it together.

anonymous · Answer

ok

akashdeepdeb · Answer

See this! http://www.purplemath.com/modules/solvquad3.htm

mathstudent55 · Answer

Let's look at choice A.
36x^2 − 18x − 9

Is the firtst term, 36x^2 a perfect square, and if so, what is it the square of?

mathstudent55 · Answer

1a. 36x^2 is a perfect square, 
1b. and it is the square of 6x.

anonymous · Answer

ok

mathstudent55 · Answer

2a. Is -9 a perfect square?
No. -9 is a negative number, and a perfect square can't be negative.
Since the answer to 2a is "no", the trinomial is not a perfect square trinomial, and there is no need to go any further.

mathstudent55 · Answer

Now we move on to choice B.
We ask the same quarions.

anonymous · Answer

okay

mathstudent55 · Answer

4a^2 − 28a − 49
1a. and 1b. 4a^2 is a perfect square and is the square of 2.
2a. -49 is negative, so it's not a perfect square.
Answer is no, this is not a perfect square trinomial.

anonymous · Answer

okay..

mathstudent55 · Answer

Let's deal with choice C.
25b^2 − 40b + 16
1a. and 1b. 25b^2 is a perfect square and is the square of 5b.
2a. and 2b. 16 is a perfect square and is the square of 4.

mathstudent55 · Answer

The way to check is this:
1. a. Is the first term a perfect square? If no, answer is no. Stop
1. b. If yes, what is the first term the square of?
2. a. Is the last term a perfect square? If no, answer is no. Stop
2. b. If yes, what is the last term the square of?
3. Is the middle term the 2 times the product of what you got in 1b and 2b?
If yes, answer is yes, it is a perfect square trinomial. If answer is no, then it isn't.

anonymous · Answer

yes?

mathstudent55 · Answer

Now look at step 3.
We have 5b and 4. The second number has to be the number whose square is 16, so 4 and -4 both work.
2 times 5b times 4 is 40b.
2 times 5b times - 4 is -40b.
The middle term of this trinomial is -40b, so it is a perfect square trinomial.

anonymous · Answer

thankyou! :))

mathstudent55 · Answer

Just to be complete, let's look at choice D.
4x^2 − 6x + 9
4x^2 is the square of 2x
9 is the square of 3 or -3
2 * 2x * 3 = 12x
2 * 2x * (-3) = -12x
The middle term of the trinomial is -6x, so it is not a perfect square trinomial.

mathstudent55 · Answer

You're welcome.