At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
First ask yourself if there is a constant you can factor out of all the coefficients. :)
Yup. So now write 4 times (whatever is left over after you factor out 4)
4(7b^2-20b-32) but then what do i do?
Now we want to factor out 7b^2-20b-32 into the product of two binomaisl: (b plus or minus stuff) times ( b plus or minus stuff). BUT LOOK! The coefficient of b^2 is 7, so that means we automatically know that it's going to look like... (7b plus or minus stuff) times (b plus or minus stuff).
well that is where i'm confused
how do i know what number to choose?
Can you factor something like: x^2 + 10x +21 ? It's similar to that, but just a little harder.
but if i factor out -32 there is nothing that would match -20
is there anything i can do?
The answer to this problem is the same as factoring something like x^2 + 10x +21 Describe how you would factor this and then the solution to your problem will make much more sense. :)
is it (x+7)(x+3) ?
Yes! :) How did you obtain that answer? How did you know to go for +7 and +3? Also, can you factor: x^2 -4x -21
well because the numbers are positive But i'm confused w/ my original problem
7b^2-20b-32 = (7b ) * ( b ) The two numbers you fill in will have to multiply to negative 32. That's the start of it.
right but there is 1*32,2*16,4*8
You have to try those out. :) ALSO note how one of those numbers is gonna be multplied by 7 when you FOIL. So it's trial and error. After a bit of practice you develop a number sense about these things. So for instance 1 * 32 won't work... (7b +32)(b -1) FOIL that out and you get 7b^2 32b -7b = -25b -31 So try the next one...
okay is it 4 and 8
In what order? And with what signs (which is + and which is - ) ?
Let's factor that out now: (7b-4)(b+8) 7b^2 (good) -4b +56b = 52b (nope) 8 * -4 = -32 (good)
You are VERY close though!
i don't know where to go from there
is it (7b-1)(b+2) ?
No, because -1 * 2 = -2. You were right, it's 4 and 8. But the order and the sign need to be tweaked.
what do u mean?
(7b )(b ) Fill in the blanks with 4 and 8. One of the combinations will work. :)
Do you know how to FOIL? (or expand) a binomial? That is the other half of solving problems like these. Going from (7b +4)(b +8) to 7b^2 +12b +32 is critical to the trial-and-error portion.
Paul's Online Math Notes has a very nice explanation of this with TONS of examples: http://tutorial.math.lamar.edu/Classes/Alg/Factoring.aspx I have to sign off, but hopefully this will help a little. :)
okay thank you!