Math Question?

Question

Factor the expression: 3x2 + 7x + 2
The answer is: (x+2) (3x+1)

How do you get this?

Answer 1

I try the reverse FOIL method.
Start with parentheses.
( )( )

Then put in the "first" components that will give you 3x^2.
You know you need this because it's given in the original equation. There's ONLY one good one that will work.

(x )(3x )

Then try to find two good ones for the "last" place.
To get 2 you can really only use 1 & 2. When you FOIL you would be multiplying these two together to get 2.

(x )(3x ) There's only two ways to try it.
(x 1)(3x 2) OR
(x 2)(3x 1) So try each and it's a + sign for both since everything in this original equation is positive +

So you have two to try out:
(x + 1)(3x + 2) OR
(x + 2)(3x + 1)

So trying to FOIL ("first" "outside" "inside" "last")
these out you get: [combine the inside and outside terms!]

(x + 1)(3x + 2) = 3x^2 +2x + 3x +2 = 3x^2 + 5x + 2
Not the original equation...

(x + 2)(3x + 1) = 3x^2 +1x +6x +2 = 3x^2 + 7x + 2 YES
This is the one. So you know that these are your factors.

Answer 2

Factoring isn't something you can ask why or how.

If someone doesn't have that perspective they can't understand it correctly. After all, factoring is mental mathematics.

Here's an easier way to factor though.

Pretend I have an expression like this:

ax^2 + bx + c

Multiply a and c. Then find the 2 factor pairs that add up to b.

3 * 2 = 6

6 + 1 = 7

Since 6 and 1 are the numbers in the factor pairs, you replace 7x with 6x + x

3x^2 + 6x + x + 2

Group them and factor

3x(x+2) + 1(x+2)

(3x+1)(x+2)

Hope that was useful.

Answer 3

First you need to set up your parentheses
(x+_)(3x+_) you know both unknowns are positive because the third term is positive, and one of your x's has to be 3 to give you the 3x^2.
Now you need two number that when multiplied equal 2 and when one is multiplied by 3, add up to 7.
2 and 1 are the only integers that when multiplied equal 2, so figure out if you can get them to sum up to 7 when one is multiplied by 3. You will find that 2*3+1=7. The 1 goes with the 3x, and the 2 goes with the x.
(x+2)(3x+1)
Check by FOILing
x(3x)+1(x)+6(x)+2=3x^2+7x+2

Answer 4

1st, factor 3x^2, --> 3x and x.
Next, factor 2, --> 2 and 1.
Make a combination of these two factors.
Try the combination of (3x + 2) and (x + 1).
Do cross multiplication.
(3x + 2) (x + 1) = 3x^2 + 3x + 2x + 2
= 3x^2 + 5x + 2 --> this is not the same as the original problem, so the combination is wrong.

Try another combination, (3x + 1) and (x + 2).
Cross multiply
(3x + 1) (x + 2) = 3x^2 + 6x +1x + 2
= 3x^2 + 7x + 2 --> this is the same as the original problem, so you got the right factors.

Answer 5

Take the answer (x+2)(3x+1), multiply the first two entries (x & 3x). This gives the 3x^2. Next, multiply the opposites and add......(IE: 3x * 2 and x * 1)....this gives 6x + 1x for 7x. Then multiply the last two entries, 2 and 1 for a product of 2.

Answer 6

first set up 2 sets of parenthesis with a 3x and x in each one because 3x^ is 3x times x to get (3x )(x )
then put in the first sign you see (the + infront of the 7x) in the set after the 3x to get
(3x+ )(x ) now for the second sign in the second set multiply the firs given sign by the second to get +x+=+ and put it in the second set

(3x+ )(x+ ) last factor the 2 into 2x1 now find out where to put the 2 and 1 to get a 7x when you foil it. try it both ways and you will find the one that works is your answer.

Answer 7

First, you know it has to be in this form :
(3x+_)(x+_).
SO, now, to find the other two numbers for the blanks.
Well, the factors of 2 are 1,2.
SO, that gives you 2 choices.
Either its (3x+2)(x+1) or (3x+1)(x+2).
Is it the first one?
No, because (3x+2)(x+1)=3x^2+3x+2x+2=
3x^2+5x+2.

So, then it has to be (3x+1)(x+2) which is the answer!