## anonymous one year ago pleaaase help.... fan and medals question in comments

1. anonymous

2. anonymous

@Michele_Laino

3. Michele_Laino

I call with F(x) the subsequent function: $F\left( x \right) = {\left( {x - 2} \right)^2}g\left( x \right)$ then, applying the product rule, we can write the first derivative of F(x) as below: $F'\left( x \right) = 2\left( {x - 2} \right)g\left( x \right) + {\left( {x - 2} \right)^2}g'\left( x \right)$ now please try to factor out x-2, what do you get?

4. anonymous

thank you.. got it.. it was so easy

5. Michele_Laino

I'm working on question #2, please wait...

6. anonymous

yes

7. Michele_Laino

here we can write this: ${x^5} + a{x^4} + 3{x^3} + b{x^2} + a = P\left( x \right){\left( {x - 2} \right)^2}$ according to the hypothesis of your problem

8. Michele_Laino

where P(x) is another polynomial. Now if I replace x with 2, I substitute x=2 into that equation, what do you get?

9. anonymous

this will be equal to 0

10. Michele_Laino

hint: the right side is: $P\left( 2 \right){\left( {2 - 2} \right)^2} = 0$

11. Michele_Laino

please write the left side after that substitution

12. Michele_Laino

hint: we have: ${2^5} + a \times {2^4} + 3 \times {2^3} + b \times {2^2} + a = 0$ please simplify

13. anonymous

32+16a+24+4b+a = 0

14. Michele_Laino

then you can simplify further: what is 32+24=... what is 16a+a=...

15. anonymous

56 and 17a

16. anonymous

i ve understood it now.. can work it/// thank you so much for your help

17. Michele_Laino

ok! so we got this condition or equation: $56 + 17a + 4b = 0$

18. Michele_Laino

:)