Posted by **JOSHI ** on Saturday, June 23, 2012 at 3:16am.

factorise:

1) x^4+10x^3+35x^2+50x+24

2) 3(a-b)(b-c)(c-a)

3) (a+b)^3-a-b

- maths -
**Reiny**, Saturday, June 23, 2012 at 8:58am
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+b-1)

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