could someone help me again?

Question

Factor the following by taking out the greatest common factor.

Factor the following by taking out the greatest common factor.

6z² +12z+14

Answer 1

Equation to solve is:

6x2+12x+14=0
The solutions are:

x1=−1+233√ix2=−1−233√i
Explanation

STEP1: Find coefficients a , b and c.

In this example a=6,b=12,c=14

STEP2: Plug in the values for a, b, and c into the quadratic formula

x1,2=−b±b2−4ac−−−−−−−√2a
x1,2=−12±122−4⋅6⋅14−−−−−−−−−−−√2⋅6
STEP3: Simplify expression under the square root.

x1,2=−12±−192−−−−√12
STEP4: Solve for x

x1=−12 + −192−−−−√12=−1+233√i
x2=−12 − −192−−−−√12=−1−233√i

Answer 2

Hi Michael.

 

The best way to find Greatest Common Factor is to go through each number and determine which prime numbers go into it.

 

6: its prime numbers are 2 and 3

 

So its factors are:

 

1, 2, 3, 6

 

12: its prime numbers are also 2 and 3

 

So its factors are:

 

1, 2, 3, 4, 6, 12

 

14: its prime numbers are 2 and 7

 

So its factors are:

 

1, 2, 7, 14

 

Then compile all of the factors:

 

1, 2, 3, 6

1, 2, 3, 4, 6, 12

1, 2, 7, 14

 

And pick the ones that show up in all of them.

 

In this case, only 1 and 2 are in every list.

 

1 * 2 = 2, so this is your GCF.

 

 

6z^2 + 12z + 14 = 2*(3z^2 + 6z + 7)

 

The 14 in there really crashed your party.

 

Hope this helps.