SOLUTION: factor by grouping: 6x^2+42x-5x-35

Algebra.Com
Question 223601: factor by grouping:
6x^2+42x-5x-35
Found 3 solutions by checkley77, jsmallt9, MathTherapy:
Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
6x^2+42x-5x-35
6x^2+37x-35
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Factoring by grouping is used on expressions of 4 or more terms. Here is a procedure for factoring by grouping:
  1. Rewrite the expression as additions. Factoring by grouping requires the Commutative (reorder) and/or Associative (regroup) Properties so we cannot have subtractions.
  2. Group the terms into groups which can be factored. This may require reordering the terms
  3. Factor each group separately using any and all appropriate factoring techniques:
    • Greatest Common Factor (GCF) (Note: Factoring by grouping is one of the few times where factoring out a 1 is done!)
    • Factoring by patterns:
    • Trinomial factoring
    • Factoring by grouping!
    • Factoring by trial and error of the possible rational roots
  4. At this point your original expression has been regrouped and each of these groups has been factored. One of the following is true:
    • There is a factor which common to each group. This is what you hope to happen. Proceed to the next step.
    • A factor or its negative is common to each group. Examples:
      • Factor: (x-3) Negative: (-x+3) or (3-x)
      • Factor (2x+5) Negative: (-2x-5)
      • Factor: (-4x-9) Negative: (4x+9)
      In this case factor a -1 out of each group which has the negative factor. If done correctly you will now have a common factor in each group and you can proceed to the next step.
    • There is no factor nor its negative in each group. In this case you have start again at step #2 and try a different grouping. (Remember: Not all expressions will factor by grouping. Once you have tried all possible regroupings and you have not been able to get a common factor at this point, it is time to give up on factoring by grouping for this expression.
  5. Factor out the factor that is common to all groups. Until you get comfortable with this step, you might want to use a temporary variable. For example, let's say our factored groups look like: :
    • Our factor which is common to each group is (x-5).
    • Let's use a temporary variable for this common factor: Let q = (x-5).
    • Replace the common factor with the temporary variable:
    • Factor out the temporary variable: q(2y+3)
    • Replace the temporary variable with the common factor: (x-5)(2y+3)
    Eventually you will not need to use a temporary variable.

Now let's try this out on your expression: :
1. Rewrite as additions

2. Create factorable groups. Since the first two terms have a common factor, 6x, and the last two terms also have a common factor, 5, we do not need to rearrange the terms. We'll just put parentheses around these two groups:

3. Factor out each group. We've already found GCF's for each group:

These groups will not factor any further so we will proceed to the next step.
4. Do we have a factor in each group which is common? The factors of the first group are 6x and (x+7). The factors of the second group are 5 and ((-x) + (-7)) so we not not have a factor common to both groups. Do we have a factor and its negative common to each group? Yes!! (x+7) and ((-x) + (-7)) are negatives of each other! So we'll factor out a -1 from the second group giving us:

which simplifies to:

Now we have a common factor, (x+7), and we can proceed.
5. Factor out the common factor. (Use a temporary variable, if needed.)

Take a good look at this:
Since this and several other "factor by grouping" questions were posted within minutes of each other I am guessing that you posted all of them. Please try this procedure on the other problems. Repost the others if you can't figure them out.


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
factor by grouping: 6x^2+42x-5x-35



----- Factoring out the GCF of each binomial expression

----- Factors of expression consist of 1 common factor and 2 commom factors
RELATED QUESTIONS

Factor by grouping... (answered by jim_thompson5910)
factor by grouping x^3 + 5x^2 - 7x... (answered by checkley77)
factor the polynominal by grouping... (answered by praseenakos@yahoo.com)
factor by grouping x^2 – 6x + 5x –... (answered by jim_thompson5910)
Factor by grouping: x2 – 6x + 5x –... (answered by wilft1,Alan3354)
factor by grouping:... (answered by Edwin McCravy)
factor by grouping... (answered by jim_thompson5910)
how do you factor 5x^5-6x^3+4x^2 by... (answered by funmath)
Factor by grouping, if possible. x^3 - 6x^2 + 5x -... (answered by stanbon)