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

label Algebra
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For the polynomial below, 3 is a zero.

f(x)= 3x^3 - 10x^2 + x + 6

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

Use fractions or square roots, not decimals.

Oct 17th, 2015

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

Since 3 is a zero, then (x - 3) is a factor

We then divide x - 3 into 3x^3 - 10x^2 + x + 6 to find the other factors.

After division we get

x^2 - x - 2   which we can factor into

(x - 2)(x + 1)

Therefore,

f(x) = (x - 3)(x - 2)(x + 1)

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

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