Question 1093352
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<pre>
x^3 + 5x < 6x^2  ====>

x^3 - 6x^2 + 5x < 0  ====>  factor left side  ====>

x*(x^2 -6x + 5) < 0  ====>  factor the quadratic polynomial  ====>

x*(x-5)*(x-1) < 0.


There are 3 critical points - the roots of the polynomial, where is becomes eqial to zero:

x = 0,  x = 1   and x = 5,

and there are 4 intervals:

(-infinity,0), where the function is NEGATIVE;

(0,1), where the function is positive;

(1,5), where the function is negative;  and

(5,infinity), where the function is positive.


Now YOU make an effort and complete the solution.
</pre>


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See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Inequalities/Solving-problems-on-quadratic-inequalities.lesson>Solving problems on quadratic inequalities</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Inequalities/Solving-inequalities-for-polynomials-factored-to-a-product-of-linear-binomials.lesson>Solving inequalities for high degree polynomials factored into a product of linear binomials</A>  

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Inequalities</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I

https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.