IF $S60 is shared in the ratio 2:3:9, the difference between the largest and the
somallest shares is

a) (x+2)(x+3)

b) x= -2 or x= -3

Step-by-step explanation:

a)

Your expression is in the form x^2+bx+c, which usually factors into some form like (x+_)(x+_). In the blank spaces, you try to find numbers that multiply to equal the last term (which is 6 in your case) and add to equal the coefficient middle term (which is 5 in your case). So, we can do a little experimenting. What are factors of 6 that add to be 5? 6 and 1? Yes, 6 and 1 multiply to be 6, but do they add up to equal 5? No. How about 2 and 3? 2 and 3 multiply to be 6 and add to be 5!

So, x^2+5x+6= (x+2)(x+3)

b) We've factored x^2+5x+6 into (x+2)(x+3). We can have an equation:

(x+2)(x+3)=0

We will work separately:

x+2=0

x=-2

x+3=0

x=-3

So, x can equal to -3 or -2.

Hope this helps