Using a given zero to write a polynomial as a product of linear factors.

label Algebra
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For the polynomial below, the -2 is a zero.

f(x)= x^3 - 2x^2 - 6x + 4

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

Use fractions or radicals in answers not decimals.

Oct 17th, 2015

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

(x^3 - 2x^2 - 6x + 4)/(x+2)=x^2-4x+2

x^2-4x+2=0

D=16-8=8

x1=(4-2sqrt2)/2=2-sqrt2

x2=(4+2sqrt2)/2=2+sqrt2

so x^3 - 2x^2 - 6x + 4=(x+2)(x-2+sqrt2)(x-2-sqrt2)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 17th, 2015

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