Ecpress g(x) as a product of linear factors from a polynomial

Algebra
Tutor: None Selected Time limit: 1 Day

For the polynomial below, -2 is a zero.

g(x)= x^3 - 2x^2 - 9x - 2

Express g(x) as a product of linear factors.

Oct 25th, 2015

Thank you for the opportunity to help you with your question!

since -2 is a zero

x^3 - 2x^2 - 9x - 2 = (x+2)(x^2 -4x-1)

x^2 -4x-1 has 2+sqrt[5] and 2-sqrt[5] as zeros

so x^2 -4x-1 = (x-2+sqrt[5]) (x-2-sqrt[5])

Hence, x^3 - 2x^2 - 9x - 2 = (x+2)(x-2+sqrt[5])(x-2-sqrt[5])

-2, 2+sqrt[5] and 2-sqrt[5] are the zeros of x^3 - 2x^2 - 9x - 2

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 25th, 2015

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