Help with this math question?

Question

It says to factor this expression:

12b squared + 17b + 6

And please don't give me JUST the answer. I want it to be explained to me so I can finish the rest of the work myself.

Answer 1

previous answer not correct--added 17b and 12b , not 12b squared + 17b + 6...

and the other answer is also incorrect--it is factorable..

Do you understand F.O.I.L.?  That's how you ended up with

12b squared + 17b + 6, you multiplied

(ab +or- b) and (xb +or- z) and you multiply the

F first

O outer

I inner

and

Last   parts

There is no surefire way of getting answer, you have to plug in and work different pairs of numbers.

The answer after mine has the correct answer, by the way.

**YOU CAN YAHOO IM ME, I USED TO TEACH MIDDLE SCHOOL MATH**

Answer 2

Looking at the expression, you are going to have two terms to multiply and both are going to have a + sign in the middle of them.  Because 6 only has 2 factor pairs (1*6 and 2*3), your answer will be either

(??b +1)(??b+6)

or

(??b+2)(??b+3)

You have to find the ??s that are factors of 12 that will make 17 in the middle when you foil.

The factor pairs of 12 are: 1&12, 2&6, 3&4

At this point, I start testing pairs. Knowing the rules of even and odd numbers, you're going to have to multiply 2 odd numbers to get an odd number, so eliminate any pairs that will not have 2 odd numbers multiplied. (That is, don't bother testing (2b+2)(6b+3) because when you FOIL them none of the terms is the product of two odd numbers).

The answer is (3b+2)(4b+3) .  Hope this is somewhat helpful.

_/

Answer 3

Ok to factorise an expression means to put it into brackets.

This expression is a trinomial, so this is how to factorise it:

(Just so you know, when I write   12b^2    it means  12b squared)

12b^2 + 17b + 6

First you multiply the first number by the last number

12 x 6 = 72

Then you have to work out what two numbers multiply to 72 and add to 17 (because 17b is the middle number)

So, we are going to use 9 and 8 because 9 x 8 = 72 and 9 + 8 = 17

then you simply write

12b^2 + 8b + 9b + 6

Now pair the first two and the last two terms together and find out what they have in common.

So 12b^2 and 8b both have  4b in common. Put that out the front of you brackets and then in the brackets write what you have to multiply 4b by to get 12b^2 and 8b. (hope that makes sense =S)

So then you have

4b(3b+2)

Then do the same for the second pair. They both have 3 in common. You then end up with:

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

Now, to simplify it and finish the process you just do this:

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

I hope that makes sense! Sorry if it doesn't =S

You can email me if you want to ask any questions

Answer 4

I do not think that it is factorable because 12, 17 and 6 do not have a common factor that can be divided among them. The b cannot alsoo be factorable. Maybe it's a trick question.

Answer 5

You have 12x^2 + 17x + 6

The answer is (4x + 3)(3x + 2)

Steps:

First, given Ax^2 + Bx + C, to factor, you need to find 2 numbers such that they multiply to AC and add up to B.

So, in 12x^2 + 17x + 6

Two numbers that multiply to 72 and add to 17 are 9 and 8. So you split up the Bx and write something like this

12x^2 + 9x + 8x + 6 (Notice that 9x + 8x = 17x so when simplified, you get the original equation)

Now, factor the first two terms and the last to terms to get:

3x(4x + 3) + 2(4x + 3)

Now notice you can factor the (4x + 3) to get

(4x+ 3)(3x + 2)

To check your answer, just multiply it back out.

This is the method to factor quadratics.

Hope this helps.

Answer 6

12b² + 17b + 6

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

First you need to know how to go the other way, that

(3b + 2)(4b + 3) multiplies to 12b² + 17b + 6

by multiplying everything in the first set of parentheses by everything in the second.

To factor, you are going in reverse.  It's kind of a puzzle.  

What factors of 12 will go with what factors of 6 to add to make 17 (you know it will be adding in this case, because there are no negatives)

12b² + 17b + 6

(factor of 12*b + factor of 6)(other factor of 12*b + other factor of 6)

12 can be 12*1 or 3*4 or 6*2

6 can be 6*1 or 3*2

I just tried out the different combinations 3*2 + 4*3, no, that's 18

3*3 + 4*2 = 9 + 8 = 17.  That works.

Here is another explanation (that might be clearer):

http://www.themathpage.com/alg/factoring...

Answer 7

add the like terms together

12b + 17b which is 29

then u add the +6

so it becomes 29b +6

i hope thats right ^_^