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Presleyram
Factor f(x) = x4 + x3 – 8x2 + 6x + 36 completely.
first see if you can guess and root by hit and trial?
Im familiar if you factor just one number out of everything, but i think you need to factor out two different numbers. @harsimran_hs4
-2 is one of the root of the equation so can you write this as (x+2) * polynomial tell me that polynomial
got hold of something?
@Presleyram i expect that you also take a initiative in solving the question rather than me doing it alone
@harsimran_hs4 (x+3) ?
agreed so now it becomes (x+3)(x+2) (some quadratic polynomial) do you know how to find this quadratic polynomial?
@harsimran_hs4 do you take a 6 out since there's a 36
no you can`t (x+3)(x+2) = (x^2 + 5x + 6) |dw:1361982840767:dw|
original polynomial is x4 + x3 – 8x2 + 6x + 36
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
@harsimran_hs4 I got (x+2)(x+3)(x2-4x+6) for the final answer
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)