SOLUTION: Find a possible middle term to make this polynomial factorable: x^2+ blank+ 20?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a possible middle term to make this polynomial factorable: x^2+ blank+ 20?      Log On


   

Question 644099: Find a possible middle term to make this polynomial factorable: x^2+ blank+ 20?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Start with several of these, with x's as "the firsts"
since x times x is x², the first term.

(x    )(x    ) 
(x    )(x    ) 
(x    )(x    )

Think of the ways to factor 20 using two factors, 1·20, 2·10, 4·5

put those in for "the lasts"    

(x   1)(x   20) 
(x   2)(x   10) 
(x   4)(x   5) 


Put +'s between because everything has a +.  Then FOIL them out

(x + 1)(x + 20) = x² + 21x +20
(x + 2)(x + 10) = x² + 12x + 20 
(x + 4)(x + 5)  = x² +  9x + 20

So the middle term could be 21x, 12x or 9x

Edwin