Question 966865


<B>Answer</B>. The roots of this polynomial are 3, -7 and -2.


<B>Solution</B>


Look for the roots of the polynomial &nbsp;{{{x^3 + 6x^2 -13x - 42}}}&nbsp; among the divisors of the constant term &nbsp;{{{42}}}.

The divisors are . . . , +/-2, +/-3, +/- 6, +/-7, . . . 


I was lucky and quickly found that &nbsp;{{{3}}}&nbsp; is the root. 

(To be honest, &nbsp;I used an Excel spreadsheet for it :) ).


Knowing it, &nbsp;you can divide your original polynomial by the binomial &nbsp;{{{x-3}}}. 

Do you know how to divide a polynomial by a binomial?

Use the same scheme as you use for dividing integer numbers &nbsp;(long division). 

After completing this, &nbsp;you will get 


{{{x^3 + 6x^2 -13x - 42}}} = {{{(x-3)}}}.{{{(x^2 + 9x + 14)}}}.


Then you can find the roots of the quadratic polynomial using the quadratic formula. &nbsp;In this way I found that the roots are -7 and -2. 


It gives the answer.