## careless850 3 years ago 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

1. careless850

Anyone? :)

2. careless850

Which ones are perfect square trinomials?

3. megan1124

a is do you know how i figured that out?

4. careless850

No, I don't.

5. megan1124

have you learned foil?

No A is not the right answer!

7. careless850

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

8. megan1124

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

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

10. careless850

I'm so confused...

11. megan1124

thats not how you do that

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

13. megan1124

noo it equals a

14. careless850

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...

15. megan1124

are you in algebra 1?

16. careless850

Yep

17. careless850

for the 3rd time.

@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 $$4a^2 − 20a + 25 = (5-2a)(5-2a) =(5-2a)^2$$

19. megan1124

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

20. careless850

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

21. megan1124

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

22. careless850

So C and D aren't?

$$49x^2 − 8x + 16$$ 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?

24. careless850

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

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

26. megan1124

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

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

28. megan1124

its a

Nope, try to solve it and see

30. careless850

There is multiple answers that can be right.

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

32. careless850

I don't know what the disciminant is.

$$25b^2 − 5b + 10$$ 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?

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

@careless850 Pls tell me if you're stuck somewhere

is it equal to zero or some other number ?

37. careless850

I'm still confused..

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

39. careless850

No.

Find it :) & check if its equal to zero

41. careless850

How do I find it?

42. careless850

......

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

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

45. careless850

no

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?

47. careless850

a is 16

yes b & c?

49. careless850

-8 is b and 1 is c.

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

51. careless850

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

Yessss good work :)

53. careless850

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

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

55. careless850

64

56. careless850

64-64 = 0

57. careless850

So it's a PST

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

59. careless850

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

60. careless850

Can you help me with another?

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

Yes its B & D

63. careless850

Thank you. :))