Answer:
x= -1 and also x = -2
Which agrees with the second option in your list of answers
Step-by-step explanation:
We look for two numbers whose product is "2" (constant term in your quadratic equation) and which added give "3" (coefficient in the middle term with "x"). So we find the factors 1 and 2:
1 times 2 = 2 and 1 + 2 = 3
So we use these factor to expand the middle term and then factor by grouping:
[tex]x^2+3x+2=0\\x^2+x+2x+2=0\\x(x+1)+2(x+1)=0\\(x+1)(x+2)=0[/tex]
Then for this product of binomials to give zero, each binomial must be zero. That is
x= -1 and also x = -2
