Question 1105806: Given that -2 is a zero of multiplicity 3 of the function P(x) = x^5 + 2x^4 - 9x^3 - 22x^2 + 4x +24 Found 2 solutions by josgarithmetic, Boreal:Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! If -2 is a zero of multiplicity 3 then part of the factorization of P is (x+2)^3. Can you work with this and continue?
You can put this solution on YOUR website! (x+2)^3 is a factor.
That is x^3+6x^2+12x+8-------------x^2-4x+3
That can be divided into x^5+2x^4-9x^3-22x^2+4x+24
==================x^5+6x^4+12x^3+8x^2---------change signs and subtract
====================-4x^4-21x^3-30x^2+4x+24
====================-4x^4-24x^3-48x^2-32x
=========================3x^3+18x^2+36x+24
=========================3x^3+18x^2+36x+24-change signs and subtract
no remainder
the quotient is x^2-4x+3, and that factors into (x-3)(x-1), so the other two roots are 1 and 3
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