12. Factor: 6b^2-b-12?

Question

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Answer 1

[7]
6b^2-b-12
=6b^2-9b+8b-12
=3b(2b-3)+4(2b-3)
=(2b-3)(3b+4)

Answer 2

Factoring (reverse FOILing) is a trial-and-error method of solving equations in the form of ax^2 + bx + c = 0.

To FOIL (FOIL = first, outside, inside, last) factors, (ax + b)(cx + d) would be:

First is ax * cx
Outside is ax * d
Inside is cx * b
Last is b*d

so we would get acx^2 +adx + cbx + bd = acx^2 + (ad+cb)x + bd

To reverse this process, we need to think of what constants we could put in for a, b, c and d such that if we FOILed the factors, we would get the original.

(to avoid confusion, I will change x for b, so we want to factor x^2 - x - 12):

(ax + b)(cx + d) = acx^2 + (ad+cb)x + bd

So we want ac = 6, ad + cb = -1. and bd = -12

For ac to be 6, our possible pairs are factors of 6: 1 and 6, or 2 and 3

For bd to be 12 (ignore the negative for now) our pairs are: 1 and 12, 3 and 4, or 2 and 6

Looking at these pairs, we can see that the only combination that makes sense is 2 & 3 for a & c and 3 & 4 for b & d (because we know we want ad and cb to differ only by 1, and using these pairs we get 8 and 9 respectively).

So now we need to figure out the sign. We know that either b or d is negative (because b * d = -12). So let's start forming our factors:

(3b ? 4)(2b ? 3)

One of the ? is + and one is -

To figure out which is - we need to look at the middle term, which is -1, so we need these to multiply to -9 and +8 so that we get the -1 when added. That means our first ? must be + and our second -

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

Here is our answer! It sounds much more complex than it is. Ignore the letters when you are trying to factor... I included them here so that you could follow the logic. Hopefully this will get you on the right track!

Best of luck! :)

Answer 3

(3b+4)(2b-3)=6b^2-b-12 first you may make a diamond. X. interior the authentic could be -seventy two by way of fact 6x-12=-seventy two then interior the backside it could be -a million by way of -b (the middle term). next you may think of up the two numbers that are components of -seventy two that upload as much as equivalent -a million. for this reason they are -9 and eight. -9x8 = -seventy two and -9=8=-1Then make the field and take out the main suitable uncomplicated multiples throughout the time of and up and down. 2b -3 _________ 3b l 6b^2 l -9b l +4 l 8b l -12 l so the respond is (3b+4) (2b-3) you need to apply the distributive supplies to envision your answer.

Answer 4

( b ) ( b )

Factor 6

3, 2 and 1, 6

Factor 12
1, 12 -- 2, 6-- 3, 4

lets look at 3,2 and 1 ,12

3-----2
...........
...........
1-----12

Go down and then go diagonal and mulitply (imagine the box, you don't have to draw it)

3,24 and 2,36 add and subtract the numbers to see if we get -1. we are not even close so try the next set

3,2
2,6

6,12 and 18,4 not close

3,2
3,4

9,8 and 6,12 we got it

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

Answer 5

6b^2-b-12
(2b-3)(3b+4)

Answer 6

6b^2-b-12
=6b^2-9b+8b-12
=3b(2b-3)+4(2b-3)
=(2b-3)(3b+4)

Answer 7

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

3b*2b=6b^2
4*2b=8b
-3*3b=-9b
4*-3=-12
6b^2-b-12

Answer 8

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