Could anyone help with this Polynomial Factoring?

Factor the polynomial (3x^5)+(11x^4)+(20x^3)+(40x^2)+32x-16=0


and write the function as a product of linear and irreducible quadratic factors with real coefficients.





I have no clue how to do this, I have tired and failed several times.





Could you help me?

Could anyone help with this Polynomial Factoring?
(x + 2)^2 (3x - 1) (x^2 + 4)
Reply:x=-2 satisfies the equation, so (x+2) is a factor. This was found by trial and error. You could also find this if you graph the equation.


Divide the ploynominal by (x+2)


]]]]]]]3x^4+5x^3+10x^2+20x-8


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x+2)3x^5+11x^4+20x^3+40x^2+32x-16


]]]]]]]]3x^5+6x^4


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]]]]]]]]]]]]]]]]]]5x^4+20x^3


]]]]]]]]]]]]]]]]]]5x^4+10x^3


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]]]]]]]]]]]]]]]]]]]]]]]]]]]]10x^3+40x^...


]]]]]]]]]]]]]]]]]]]]]]]]]]]]10x^3+20x^...


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The given polynomial, therefore , can be factored as


(x+2)(3x^4+5x^3+10x^2+20x-8)


x = 0.67242731 is a root of the equation


3x^4+5x^3+10x^2+20x-8, but this doesn't help factor it with integer coefficients.
Reply:airforcesigop did it right. I'd like to know HOW he got it. I couldn't!

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