maths
posted by JOSHI .
factorise:
1) x^4+10x^3+35x^2+50x+24
2) 3(ab)(bc)(ca)
3) (a+b)^3ab

1. use the factor theorem
looking at 24, I tried ±1, ±2, ...
and found that x=1 and x=2 worked
so I used synthetic division consecutively and found
x^4+10x^3+35x^2+50x+24
= (x+1)(x+2)(x^2 + 7x + 12)
and the quadratic factors again, so the final factors are
(x+1)(x+2)(x+3)(x+4)
2. already fully factored
3. (a+b)^3  a  b
= (a+b)^3  (a+b)
= (a+b)( (a+b)^2  1) , last part is difference of squares
= (a+b)(a+b+1)(a+b1)