Answer:
x = - 2, - 3
Explanation:
x² + 5x + 6
to find the zeros equate f(x) to zero, that is
x² + 5x + 6 = 0
consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
the factors are + 2 and + 3 , since
+ 2 × + 3 = + 6 and + 2 + 3 = + 5
use these factors to split the x- term
x² + 2x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )
x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 2 = 0 (subtract 2 from both sides )
x = - 2
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
the zeros are x = - 2, - 3