factor the following trinomials m² + 7m + 12=

Question

I need help

 

Answer 1

factor the following trinomial m² + 7m + 12=

 

=m^2+3m+4m+12=m(m+3)+4(m+3)=(m+3)(m+4)

Answer 2

Remember that:    (x + a)*(x + b)  =   x² + bx + ax + ab

                                                    =  x² + (a+b)x + ab

 

So when the problem is to factor  m² + 7m + 12,  we must find two numbers whose sum (a+b)=7 and whose product (ab)=12.  And, if need be, we can find the prime factors of each value to help identify the possibilities.

 

However, 3+4=7 and 3*4=12 come to mind rather quickly.

    m² + 7m + 12 = (m+3)(m+4)                  [check this using FOIL]

Answer 3

First notice the factors of 12 are 6*2, 4*3,12*1 also notice the sum of 4 and 3=7 so the factors are (M+3)(M+4)

 

In general if the coefficient of the squared term is 1 then x² + ax + b can be factored into (x+c)(x+d) if c+d=a and c*d=b so the trick is to find the two numbers c and d the satisfy these relations, it's trial and error and if a and b are small its easy.

 

Hope this helps

 

Jim

Answer 4

Dear Shamera,

      When you have all plus signs in the quadratic, you will have factors with all plus signs.  Let me give you a different example that is the same as yours:

 

X² +4x +3=0           What factors when multiplied will give you 3, the last term?    1*3

 

                                 Now, if you add 1X +3X=4X  the middle term

 

 

(X+3)(X+1)=0          You can check this answer by multiplying the two factors together.

 

 

 

Let's look at your problem:    m² +7m + 12.      What factors for the last term will give you 12?

 

                                                                1*12,    6*2,   and 3*4

 

Try adding the factors to see if you come out with the middle term.  For example, 1+12 =13, but the middle term is 7m.

 

 

I will let you finish this problem.  If I have helped you, please give me a thumbs up.

 

                                                                                     Susan C.

Answer 5

To factor a trinomials  ax^2+bx+c=0

 

when a =0, you have to find two number that when multiply equals "c" and when add equals "b".

 

Look for the factors of c=12  > 3x4=12       these factors work because 3+4=7 

 

so the answer is >     m^2+7m+12= (m+4)(m+3)

 

hope this helps!

regards

Carmen