Question 1011576
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f(x)=2x^3+5x^2-x-6

I need to find the actual zeros on my calculator. Then, show the correct factorization of the function. Thanks.
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<pre>
{{{2x^3+5x^2-x-6}}} = {{{0}}}.

It is easy to check that x = 1 is the root.

Further, it means that the left side polynomial has a factor (x-1).

Make the long division of {{{2x^3+5x^2-x-6}}} by x-1.

You will get the quadratic polynomial as the quotient.

Then find its roots.

And the last thing. Do you know that if {{{x[1]}}}, {{{x[2]}}} and {{{x[3]}}} are the roots of a polynomial of the third degree, 
then this polynomial is the product {{{a*(x-x[1])*(x-x[2])*(x-x[3])}}}, 
where a is its leading coefficient at {{{x^3}}} ?

That is all.
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