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2x^2+23x+11

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2 Answers

Problems such as this (factoring quadratic expressions) can be easily solved by a technique called grouping.  First factor out any common constant factors out.  In the given problem there are no common constant factors, so we proceed to next step.  
 
The coefficient of x2 is 2 (a in ax^2 + bx + c) and the constant is 11.  First multiply 11 by 2 (a * c).  11 * 2 = 22.
 
Now look at the coefficient for  x.  It is 23.  Now what two factors when multiplied yield 22 and when added yield 23?  22 and 1.  Now write the 23x as 22x + x.  So the expression now becomes 
 
2x^2+22x+x+11
 
Now group the first two terms together and the last two together and factor out common terms to make the expression look like below
 
2x(x + 11) + 1(x+11)
 
Taking the common factor x+11 out, we get the final result for the expression as
 
(x+11)(2x+1)
Hi Griin;
I am guessing you need this factored.
2x2+23x+11
For the FOIL, we know that...
FIRST must be (2x)(x)
LAST must be (11)(1) or (1)(11)
INNER and OUTER must add-up to 23x; 2(11)x+1x=23x
So...
(2x+1)(x+11)
Let's FOIL
FIRST...(2x)(x)=2x2
OUTER...(2x)(11)=22x
INNER...(1)(x)=x
LAST...(1)(11)=11
2x2+22x+x+11
2x2+23x+11
 
Is this the answer you need?  If not, please let me know.