SOLUTION: how would you factor? also check the factors? need to understand a^2+7a+12=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how would you factor? also check the factors? need to understand a^2+7a+12=0      Log On


   

Question 427099: how would you factor? also check the factors? need to understand
a^2+7a+12=0
Found 2 solutions by ewatrrr, dnanos:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

factoring

a^2+7a+12=0

(a+4)(a+3)= 0

Note:SUM of the inner product(4a) and the outer product(3a) = 7a

(a+4)=0    a = -4

(a+3)= 0   a = -3



CHECKING our Answer*** SUBSTITUTING our Answers back into the original Equation

a^2+7a+12=0

16 -28 + 12 = 0  |checking a = -4

9  -21 + 12 = 0  |checking a = -3

Answer by dnanos(83) About Me  (Show Source):
You can put this solution on YOUR website!
I would use the discriminant :
That is for ax^2+bx+c=0
the discriminant is b^2-4ac
a=1, b=7, c=12
b^2-4ac=7%5E2-4%2A1%2A12=49-48=1
the zeros are for %28-7%2B-sqrt%281%29%29%2F%282%2A1%29=(-7+-1)/2
a%5B1%5D=-3 a%5B2%5D=-4
Factorize:
%28a-%28-3%29%29%28a-%28-4%29%29=0
%28a%2B3%29%28a%2B4%29=0.
You may also write directly
a%5E2%2B3a%2B4a%2B12=0
a%28a%2B3%29%2B4%28a%2B3%29=0
%28a%2B3%29%28a%2B4%29=0
so
a+3=0 or a+4=0
That is
a=-3 or a=-4