Question 215406
Factor the polynomial


{{{15s^3-21s^2+18s}}}


Step 1.  Factor out 3s in the three terms.  That is, {{{3s*(5s^2-7s+6)}}}


Step 2.  Need to find two integers m and n such that their product is mn=5*6=30 and their sum is m+n=-7.


Step 3.  After several tries, the numbers are no numbers that satisfy step 2.  Note if equation was {{{3s*(5s^2-7s-6)}}} then the numbers would be -10 and 3 for the quadratic expression.  We can factor with grouping where {{{-7s=-10s+3s}}} and


{{{(5s^2-10s)+(3s-6)= 5s(s-2)+3(s-2)=(5s+3)(s-2)}}}.


Then the factor for this changed problem yields: {{{15s^3-21s^2-18s=3s(5s+3)(s-2)}}}



Step 4. We can use the quadratic formula given as 


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


where a=5, b=-7 and c=6.


*[invoke quadratic "x", 5, -7, 6  ]


Step 5.  We have imaginary results for this example and there are no real solutons.


I hope the above steps and explanation were helpful. 


For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry. 


Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.


Respectfully, 
Dr J