Show that (x+2)(x+3)(x+5) can be written in the form ax^3 + bx^2 + cx +d, where a,b, c and d are positive integers
I would tell them to start multiplying out the first brackets (x+2)(x+3)! I would do this by timesing x by everything in the second bracket and then 2 by everything in the second brakcet! Giving the answer x2 + 3x + 2x + 6! Then I would explain because 3x are both factors of x, they can be added together as 5x! So i would now times my answer that I have just got to the third bracket! (x2+ 5x+ 6)(x+5)and now I would use the same method as before by timesing each bit of the second bracket by x2 ,giving x3 + 5x2 Then times everything in the second bracket by 5x, giving 5x2 +25x! and then finally timesing the second bracket by 6! Giving 6x + 30 !
Now if put it all together I have x^3 + 5x^2 + 5x^2 + 25x + 6x +30! And if we add all the integers that have he same factor, for example 25x + 6x will go together to me 31x, we got x^3 + 10x^2 +31x +30
