Math Is Fun Forum

Rudy

Guest

Help With Factoring

Can someone help me solve this equation, please?

9x^3 + 18x^2 - 4x - 8 = 0

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Help With Factoring

By inspection, -2 looks like it would work.

f(-2) = 9(-2)³+18(-2)² - 4(-2) - 8
        = 0

Therefore -2 is a solution. If x=-2 is a solution, then x+2 is a root. Dividing the equation by x+2 (using long division) gives:

9x² - 4

which can be factorised to give (3x+2)(3x-2)

Therefore 9x³+18x² - 4x - 8 = (x+2)(3x+2)(3x-2), so the solutions are -2, -2/3 and 2/3.

Last edited by Daniel123 (2008-01-13 04:50:00)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,326

Re: Help With Factoring

9x^3 + 18x^2 - 4x - 8 = 0
Looking at the equation, it can be simplified as

9x^2(x+2)-4(x+2) = 0
(9x^2-4)(x+2) = 0
Further simplifying 9x^2-4,
(3x-2)(3x+2)(x+2) = 0.

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Rudy

Guest

Re: Help With Factoring

Thank you very much for your help, guys.