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Presleyram

  • 2 years ago

Factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely.

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  1. harsimran_hs4
    • 2 years ago
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    first see if you can guess and root by hit and trial?

  2. Presleyram
    • 2 years ago
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    Im familiar if you factor just one number out of everything, but i think you need to factor out two different numbers. @harsimran_hs4

  3. harsimran_hs4
    • 2 years ago
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    -2 is one of the root of the equation so can you write this as (x+2) * polynomial tell me that polynomial

  4. harsimran_hs4
    • 2 years ago
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    got hold of something?

  5. harsimran_hs4
    • 2 years ago
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    @Presleyram i expect that you also take a initiative in solving the question rather than me doing it alone

  6. Presleyram
    • 2 years ago
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    @harsimran_hs4 (x+3) ?

  7. harsimran_hs4
    • 2 years ago
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    agreed so now it becomes (x+3)(x+2) (some quadratic polynomial) do you know how to find this quadratic polynomial?

  8. Presleyram
    • 2 years ago
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    @harsimran_hs4 do you take a 6 out since there's a 36

  9. pattycake3
    • 2 years ago
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    yes!

  10. harsimran_hs4
    • 2 years ago
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    no you can`t (x+3)(x+2) = (x^2 + 5x + 6) |dw:1361982840767:dw|

  11. Presleyram
    • 2 years ago
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    @harsimran_hs4 1

  12. harsimran_hs4
    • 2 years ago
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    original polynomial is x4 + x3 – 8x2 + 6x + 36

  13. harsimran_hs4
    • 2 years ago
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    this division is tricky so think over it with cool mind and in the end remainder must be zero so find out take your time and then reply

  14. Presleyram
    • 2 years ago
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    @harsimran_hs4 I got (x+2)(x+3)(x2-4x+6) for the final answer

  15. harsimran_hs4
    • 2 years ago
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    great!! so now to factorize x^2 -4x + 6 is not factorisable because the discriminant of this equation is -ve i.e it results in complex( non real) roots (although i think you already figured that out) so final answer is (x+2)(x+3)(x2-4x+6)

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