SOLUTION: I don't understand how to do this... REWRITE THE MIDDLE TERM AS THE SUM OF TWO TERMS AND THEN FACTOR COMPLETELY. 4Z^3 - 18Z^2 - 10Z

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I don't understand how to do this... REWRITE THE MIDDLE TERM AS THE SUM OF TWO TERMS AND THEN FACTOR COMPLETELY. 4Z^3 - 18Z^2 - 10Z      Log On


   

Question 44878: I don't understand how to do this...
REWRITE THE MIDDLE TERM AS THE SUM OF TWO TERMS AND THEN FACTOR COMPLETELY.
4Z^3 - 18Z^2 - 10Z
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
4Z%5E3+-+18Z%5E2+-+10Z
= 2Z%282Z%5E2+-+9Z+-+5%29

So we have to factorise 2Z%5E2+-+9Z+-+5.

See my solution to the problem mentioned below for more detailed conception of how to solve such problems.
http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=44877

1. 2 x (-5) = -10
2. 1 x (-10) = -10 and -9 = 1 + (-10)
3. Given expression: 2Z%282Z%5E2+%2B+Z+-+10Z+-+5%29.
4. Taking common terms in brackets: 2Z%28Z%282Z+%2B+1%29+-+5%282Z+%2B+1%29%29.
5. Re-writing the expression we get the factors: 2Z%282Z+%2B+1%29%282Z+-+5%29.