y^3-11y^2+28y

Select the correct choice below.

(a) y^3-11y^2+28=?

(b) The polynomial is prime.

y^3-11y^2+28y

Select the correct choice below.

(a) y^3-11y^2+28=?

(b) The polynomial is prime.

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You have two slightly different polynomials showing.

y^{3} - 11y^{2} + 28y factors since you can pull out y to get y(y^{2} - 11y + 28).

Then noticing that -7 + (-4) = -11 and (-7)(-4) = 28, you get y(y - 4)(y - 7).

The other one you have is y^{3} - 11y^{2} + 28 which you can try the rational root test on.

The candidates are x = ±1, ±2, ±4, ±7, ±14, ±28. None of these turn out to be roots so it won't factor.

Another interesting problem is finding roots of any cubic polynomial. If you are curious on how to do that, you can check out my two-part video lesson.