Use factoring

Question

factor. Use factoring by grouping even though it would seem reasonable to first combine like terms . 

 

6s^2+4s+9s+6=

Answer 1

6s² + 4s + 9s + 6

(6s² + 4s) + (9s + 6)

2s(3s + 2) + 3(3s + 2)

(2s + 3)(3s + 2)

Answer 2

Dan, we are going to factor out what the first two terms, then the last two terms, have in common.

 

What does 6s² + 4s have in common? 2s. Factoring out 2s, we get 2s(3s + 2).

 

What does 9s + 6 have in common? 3. 3(3s+ 2).

 

So, now if we write it all out...

 

2s(3s + 2) + 3(3s + 2).

 

Notice, we have 3s + 2 twice. This means that 2s and 3 are "like terms" because they are both being multiplied by 3s + 2.

 

We still can't add 3s + 2, though, so they stay separate in their own set of parantheses.

 

Our final answer is (2s + 3)(3s + 2).

 

Hope this helps!

Answer 3

= (3s+2)(2s+3) because, when you FOIL, the Outer product is 9s and the inner product is 4s & these combine to get the right answer.

 

As a general rule, students should be weaned from specific instructions on how to solve problems; instead, just being told to factor is best, so that students can work it out by any method that they know--because in real life, problems show up without labels.

 

I do recognize that the present teaching methods have become somewhat dictatorial, and perhaps they should be in the beginning, but the sooner weaned, the better.  Similarly, when quadratic equations arise, people should (ASAP) simply be told to Solve. Then they would normally attempt factoring; if difficult, they should switch to the quadratic formula.