polynomial: factoring 12mb - 9m + 8b - 6 completely

[nae]

I need help finding out what this polynomial is equal to when completely factored.

. . .12mb - 9m + 8b - 6

Here's what I came up with so far:

. . .(3)(4)(m)(b) - (3)(3)(m) + (2)(4) - (3)(2)

. . .(3)(2)(2)(m)(b) - (3)(3)(m) + (2)(2)(2)(3)(2)

. . .3(4mb - 3m + 4 - 4)

Then I get lost.

I really dont know if I did these steps right. Could someone please help me? Thank you!

 

[stapel]

Since 3 isn't a factor of 8, you know that 3(4mb - 3m) cannot be correct. (Note that "+4 - 4" equals zero. In other words, your answer actually has only two terms, not four. Half of the polynomial has disappeared somehow.)

. . .12mb - 9m + 8b - 6

Here's what I came up with so far:

. . .(3)(4)(m)(b) - (3)(3)(m) + (2)(4) - (3)(2)

What happened to the "b" in the third term?

. . .(3)(2)(2)(m)(b) - (3)(3)(m) + (2)(2)(2)(3)(2)

How did "+ 8b - 6" turn into "2×2×2×3×2"? What happened to the variable and the signs?

Also, they should have covered in class that this is not looking for some factor to come out of all of the terms. Instead, they are looking for something in the form "(r + p)(s + q)". For instance:

. . . . .3fg + 15f - 2g - 10

. . . . .(3fg + 15f) - (2g + 10)

. . . . .3f(g + 5) - 2(g + 5)

. . . . .(g + 5)(3f - 2)

Use the above sort of factoring technique to complete this exercise.

Eliz.