## anonymous one year ago WILL FAN AND MEDAL Select the polynomial that is a perfect square trinomial. 49x2 − 8x + 16 4a2 − 10a + 25 25b2 − 5b + 10 16x2 − 8x + 1

1. anonymous

a number after the variable is an exponent

2. anonymous

@mathway

3. anonymous

@Maxmius @mbma526

4. Taylor0402

5. anonymous

I can't click the link @Taylor0402

6. Taylor0402

copy and paste if u doof

7. anonymous

@ospreytriple

8. anonymous

allo ospreytriple :)

9. anonymous

Hi. You need some help? Firstly, for a trinomial to be a perfect square, both the first and last terms must be perfect squares. For example$\left( 2x+3 \right)\left( 2x+3 \right) = 4x^2+12x+9$Both the first term, 4x^2, and the last term, 9, are perfect squares. Understand so far?

10. anonymous

yes @ospreytriple

11. anonymous

This will eliminate one of the answers.

12. anonymous

Now, to pin it down, The coefficient of the middle term (the coefficient of the 'x' term) must be equal to twice the product of the square roots of the coefficient of the first term and the third term. In my example$4x^2+12x+9$the square root of the coefficient of the first term is 2 and the square root of the third term is 3. Twice their product is 2(2 x 3) = 12. OK?

13. anonymous

And to make it even trickier, you have to consider that the negative square root may also be a possibility.

14. anonymous

Take the first answer given for example. The square root of 49 is +7 or -7 and the square root of 16 is +4 or -4. So, if it is a perfect square the coefficient of the middel term must be one of 2(-7 x 4) 2(-7 x -4) 2(7 x 4) 2(7 x -4) If it is not one of these, the it is not a perfect square trinomial.

15. anonymous

BTW these are the answers 49x2 − 8x + 16 4a2 − 10a + 25 25b2 − 5b + 10 16x2 − 8x + 1

16. anonymous

@ospreytriple is it B?

17. anonymous

@ospreytriple

18. anonymous

Yes. Well done.

19. anonymous

THX SO MUCH

20. anonymous

Oops. sorry, it's not B.

21. anonymous

The middle coefficient must be TWICE the product of the two square roots.

22. anonymous

So d

23. anonymous

So, for the possibilities for the coefficient of the middle term are 2(-2 x 5) 2(-2 x -5) 2(2 x 5) 2(2 x -5)

24. anonymous

Yes, D is correct. Sorry for the mixup.

25. anonymous

its ok