SOLUTION: This is from a worksheet. I cannot figure this one out at all. y^3+5y^2-9y-45 The instructions are to factor completely.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This is from a worksheet. I cannot figure this one out at all. y^3+5y^2-9y-45 The instructions are to factor completely.      Log On


   

Question 87646: This is from a worksheet. I cannot figure this one out at all.
y^3+5y^2-9y-45
The instructions are to factor completely.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
time to be a little sneaky then...
+y%5E3%2B5y%5E2-9y-45+
or...
+y%5E3-9y+%2B5y%5E2-45+
so think about the 2 sets of terms, bracketed:
+%28y%5E3-9y%29+%2B+%285y%5E2-45%29+
+y%28y%5E2-9%29+%2B+5%28y%5E2-9%29+

and you notice that both factorised terms have a common term which can be factorised out, giving us:
+%28y%5E2-9%29%28y%2B5%29+

The first term is a difference of 2 squares so:
+%28y%2B3%29%28y-3%29%28y%2B5%29+

there you go :-)

cheers
Jon