Answer:
x = - 4, x = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
3x² + 14x + 8 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 + 8 = 24 and sum = + 14
The factors are + 12 and + 2
Use these factors to split the x- term
3x² + 12x + 2x + 8 = 0 ( factor the first/second and third/fourth terms )
3x(x + 4) + 2(x + 4) = 0 ← factor out (x + 4) from each term
(x + 4)(3x + 2) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]
