Melody

Thanks Ginger :)

Thanks for giving that comprehensive answer  

I suspect there is a little problem with the English language here.

Half a sphere is a hemisphere

but

Half a circle is a semicircle.    

Don't ask me why ://

There is another similar question here    (sept 17)

I found an old question that was a bit like this, I remember Bertie helped me with it. 

(1) A line segment is broken at two random points along its length. What is the probability that the three new segments can be arranged to form a triangle?

I stuffed up on question 1 but it is very similar to question 2

Since you have never bothered to respond to my answers there is not point in me doing it properly now.

I am glad I could help. 

You can expand your final answer to see if it is correct or not.

It is always good to check answers :)

\(3x^2+5x+2\\ \)

First you need to find two numbers that multiply to give 3*2=6  

Obviously they need to be of the same sign (positive or negative)

They also need to add to 5.    Since 5 is positive both numbers must be positive.

2 and 3 work

2+3=5

2*3=6

so now you need to write 5x as 3x+2x

\(3x^2+5x+2\\ =3x^2+3x+2x+2\\ =3x^2+3x\quad+\quad2x+2\\ \text{Now factor in pairs}\\ =3x(x+1)\quad + \quad 2(x+1)\\ =(3x+2)(x+1) \)

Thanks Heureka   

Thanks Bob I really appreciate your answer. 

I shall give what you say a lot of thought.