# SOLUTION: Factor completely. If the polynomial is prime, state this. -3b-88+b^2

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Factor completely. If the polynomial is prime, state this. -3b-88+b^2       Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Polynomials, rational expressions and equations Solvers Lessons Answers archive Quiz In Depth

Question 165723: Factor completely. If the polynomial is prime, state this.
-3b-88+b^2

You can put this solution on YOUR website!

Rearrange the terms.

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 1 and the last term -88 to get -88. Now we need to ask ourselves: What two numbers multiply to -88 and add to -3? Lets find out by listing all of the possible factors of -88

Factors:

1,2,4,8,11,22,44,88,

-1,-2,-4,-8,-11,-22,-44,-88, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -88.

(-1)*(88)=-88

(-2)*(44)=-88

(-4)*(22)=-88

(-8)*(11)=-88

Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3

||||||||
 First Number | Second Number | Sum 1 | -88 | 1+(-88)=-87 2 | -44 | 2+(-44)=-42 4 | -22 | 4+(-22)=-18 8 | -11 | 8+(-11)=-3 -1 | 88 | (-1)+88=87 -2 | 44 | (-2)+44=42 -4 | 22 | (-4)+22=18 -8 | 11 | (-8)+11=3

We can see from the table that 8 and -11 add to -3. So the two numbers that multiply to -88 and add to -3 are: 8 and -11

breaks down to this (just replace with the two numbers that multiply to -88 and add to -3, which are: 8 and -11)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 1b out of the first group and factor a -11 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
==============================================================================