more info please

Question

1.) x^2+6x+2x+12=0                        Given

2.) x^2+8x+12=0                             Reason substitution

3.) (x+6)(x+2)=0                              Reason distributive postulate

4.) x+6=0 or x+2=0                          Reason  zero product postulate

5.) x=-6 or x=-2                               Reason   subtraction property          

                                                                   of equality

How do you get from step two to step three?

Answer 1

Hi Pam

 

1.) x^2+6x+2x+12=0      Given
2.) x^2+8x+12=0            Reason substitution <----I would call this addition, not substitution
3.) (x+6)(x+2)=0             Reason distributive postulate
4.) x+6=0 or x+2=0         Reason zero product postulate
5.) x=-6 or x=-2               Reason subtraction property of equality

 

Step 3 is a factoring of the quadratic in step 2.

 

Since the 2nd operation is positive, we know the operations in the factors are the same.  Since the 1st operation is also positive, that tells us the operations in the factors are both addition.

The numbers that are added to x must satisfy BOTH of the following.

1) Multiply them and get 12

2) Add them to get 8.

 

I hope this helps.