Answer:
x = - 3, x = - 2, x = 0
Explanation:
Given
x³ + 5x² + 6x ← factor out x from each term
= x(x² + 5x +6) ← factor the quadratic
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 , thus
x² + 5x + 6 = (x + 2)(x + 3) , and
f(x) = x³ + 5x² + 6x = x(x + 2)(x + 3)
To find the zeros equate f(x) to zero, that is
x(x + 2)(x + 3) = 0
Equate each factor to zero and solve for x
x = 0
x + 2 = 0 ⇒ x = - 2
x + 3 = 0 ⇒ x = - 3
Zeros from least to greatest are x = - 3, x = - 2, x = 0