Answer:
see explanation
Step-by-step explanation:
3x² + 5x + 2 = 0
(a)
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 × 2 = 6 and sum = 5
The factors are + 3 and + 2
Use these factors to split the x- term
3x² + 3x + 2x + 2 = 0 ( factor the first/second and third/fourth terms )
3x(x + 1) + 2(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(3x + 2) = 0
(b)
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]
