If someone could help me with these last few problems, it would be nice. Check all polynomials that are perfect square trinomials:
A) 49x^2 − 8x + 16
B) 4a^2 − 20a + 25
C) 25b^2 − 5b + 10
D) 16x^2 − 8x + 1

- anonymous

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- anonymous

Anyone? :)

- anonymous

Which ones are perfect square trinomials?

- anonymous

a is do you know how i figured that out?

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## More answers

- anonymous

No, I don't.

- anonymous

have you learned foil?

- Diyadiya

No A is not the right answer!

- anonymous

Diya, there is more than one I can choose for the right answer. How come A isn't one of them?

- anonymous

|dw:1338062447129:dw| that is y it is

- Diyadiya

If \( ax^2+bx+c \) is a perfect square trinomial then the discriminant will be zero.
Do you know to find the discriminant?
\( D= b^2- 4ac =0\)

- anonymous

I'm so confused...

- anonymous

thats not how you do that

- Diyadiya

@megan1124 (7x-4)(7x-4) = 49x^2-56x+16

- anonymous

noo it equals a

- anonymous

um.. Can someone just show me how to do these or.. if you are going to argue.. just give me a hint to the right answers please...

- anonymous

are you in algebra 1?

- anonymous

Yep

- anonymous

for the 3rd time.

- Diyadiya

@careless850
Lets check the second option
\( 4a^2 − 20a + 25 \) this is of the form \( ax^2+ bx + c \)
Now find \(b^2-4ac \)
\(b^2-4ac = (-20)^2- 4*4*25= 400-400 = 0 \)
Now verify if your answer is right
\( 4a^2 − 20a + 25 = (5-2a)(5-2a) =(5-2a)^2 \)

- anonymous

ok thanks its and b :) because you can divide the first one and last one by a number and get the same number you divided by and get a whole number

- anonymous

O.o what? So is one of the answers A or is one B?

- anonymous

the 2 answers are a and b because if you factor them you don't get more that 2 numbers like the one i showed you above earlier

- anonymous

So C and D aren't?

- Diyadiya

\( 49x^2 − 8x + 16 \)
Find \(b^2 -4ac \)
b=-8 , a=49 , c=16
\(b^2 -4ac = (-8)^2 - 4(49)(16) = -3120 \)
So option A is not the right answer
Can you check for C now?

- anonymous

Diya, A isn't right? So the only right answer is B?

- Diyadiya

A isn't Right! i just showed you why..
B is right
But you have to check the others too

- anonymous

you can have more than one right answer right? if so its a and b

- Diyadiya

@megan1124 A is not the right answer
Can you tell me what is (7x-4)(7x-4) ??

- anonymous

its a

- Diyadiya

Nope, try to solve it and see

- anonymous

There is multiple answers that can be right.

- Diyadiya

Can you find the discriminant of C & D ?
\( D= b^2-4ac \)

- anonymous

I don't know what the disciminant is.

- Diyadiya

\( 25b^2 − 5b + 10\) this is of the form \( ax^2 + bx +c \)
|dw:1338063436660:dw|
so
a =25
b=-5
c=10
Now find Dicriminant \( D =b^2-4*a*c\)
Can you do that?

- Diyadiya

Just plug in the values of a ,b & c in the equation \(b^2 - 4ac \)
can you ?

- Diyadiya

@careless850 Pls tell me if you're stuck somewhere

- Diyadiya

is it equal to zero or some other number ?

- anonymous

I'm still confused..

- Diyadiya

where are you stuck ? did you find b^2 -4ac?

- anonymous

No.

- Diyadiya

Find it :) & check if its equal to zero

- anonymous

How do I find it?

- anonymous

......

- Diyadiya

25b^2 − 5b + 10
Given :
a =25
b=-5
c=10
b^2 - 4ac

- Diyadiya

(-5)^2 - 4* 25 * 10
is it equal to zero?

- anonymous

no

- Diyadiya

so its not a perfect square trinomial
Now do the last one
D) 16x^2 − 8x + 1
Can you tell me what is a ,b & c here?

- anonymous

a is 16

- Diyadiya

yes
b & c?

- anonymous

-8 is b and 1 is c.

- Diyadiya

Right!!!!!!!
Now Find the discriminant
How do you find it?

- anonymous

So I would do this.. -> -8^2 -4*16*1.

- Diyadiya

Yessss good work :)

- anonymous

how to solve that, I don't know, but that's the problem.. lol

- Diyadiya

\( (8)^2 - 4 \times 16 \times 1 \)
What is \( 8^2 \) ?

- anonymous

64

- anonymous

64-64 = 0

- anonymous

So it's a PST

- Diyadiya

Yess!! so its a perfect square trinomial :)
You can verify by factoring ^_^

- anonymous

I see. Pretty easy now I guess. So the only ones that are perfect square trinomials are B and D?

- anonymous

Can you help me with another?

- Diyadiya

Yes, If you factorise 16x^2 − 8x + 1 you'll get (1-4x)(1-4x) = (1-4x)^2
Post it as a new question :)

- Diyadiya

Yes its B & D

- anonymous

Thank you. :))

- Diyadiya

Np :)

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