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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 -

    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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